The 42-year-old ended a five-year drought with victory at the Tour Championship on Sunday.
But Bjorn insists Europe are not apprehensive about facing Woods – or any of his stellar United States team-mates.
Woods has rocketed from world No 1,173 last December to 13th after finally breaking his barren spell at the PGA Tour’s season-ending event.
He saw off the challenge of the likes of Justin Rose, Rory McIlroy, John Rahm, Tommy Fleetwood and Paul Casey at East Lake, but that does not mean Europe’s Ryder Cup players will feel any inferiority at Le Golf National this week.
“We don’t fear anyone because we’ve played against them so many times before individually, but we respect our opponents and know what we are up against,” said Bjorn.
“That, I think, is key to all this. We’ll go out and do what we can and play our game.
“What stands on the other side we know is one of the strongest American teams of all time.
“We do what we do as a European team and then we go out and take that onto the golf course – and that’s all 12 Americans.
“It’s not one individual, it’s the whole team we are up against.”
The United States team comprises six of the world’s top 10 and 11 of the top 17, including No 1 Dustin Johnson, No 3 Brooks Koepka and No 4 Justin Thomas.
But none carry the weight that Woods does even if his Ryder Cup record is poor by his previously high standards.
In seven appearances he has won 13 and lost 17 of his 33 matches, including just half a point from four matches on his last appearance, in 2012.
Much of that was put down to his singular, often aloof attitude in the past that did not lend itself to a team environment.
But after back fusion surgery threatened to end Woods’s career he has returned a different, more approachable character and many of his team-mates hung around at East Lake to see him win.
“Tiger played so well at The Tour Championship and to grab a hold of the golf tournament early and fend everyone off, I think was a good buzz in the team room,” said USA captain Jim Furyk.
“A lot of the guys stayed out there at the course to congratulate him.
“He’s played really well all year, I think. (He’s) been knocking on the door at two majors and had a number of opportunities to win this year.
“When you look at now, maybe comparing past Ryder Cups to this one, I think what’s so special is Tiger has engrained himself in our team atmosphere and became such a big part of the team in 2016 as a vice-captain, and then again in 2017 as an assistant captain at the Presidents Cup.
“I think it’s special for him now to kind of join these younger players as a team-mate. You know, he won [on Sunday] as an individual and I know how much that means to him and how important it was, but he’s flipped that page pretty quickly and is really excited to join his team-mates and move forward in that process.”
Even Bjorn had to admit he was pleased to see Woods back in the winners’ circle.
“I spent 25 years playing professional golf with Tiger Woods and any time he does anything great that’s a story and that’s where we want to see him,” he said.
“We want to see him at the top of the game. He does so much for the game of golf. It was great for the greater aspect of the game.
“Him winning golf tournaments is something that’s brilliant and I think we all benefit from it because, in the end, whatever it is these 24 guys are going to do this week the game of golf needs that boost of somebody like him that transcends the game to the masses, needs him at the top of the game. So for everyone in golf, it’s brilliant.”
Bjorn believes his pep talks with wild-card pick Sergio Garcia have had the desired effect ahead of this week’s Ryder Cup.
Garcia was a controversial choice after a poor run of form, the 2017 Masters champion missing the cut in his last five major starts and failing to qualify for the FedEx Cup play-offs on the PGA Tour. The 38-year-old did finish eighth in the French Open at the Ryder Cup venue of Le Golf National, but that had been his only top-10 finish since early March before a closing 65 on Sunday gave the experienced Spaniard a tie for seventh in the Portugal Masters.
“I was pleased for Sergio,” Bjorn said. “I think he felt more than I did that he wanted to get out there and shoot some good numbers and feel good about himself on the golf course.
“I know what Sergio stands for and I know what he brings to this team. Sergio is the type of guy that sometimes needs that little boost of feeling like things are going his way.
“I think the conversations I had with him leading into picking him, and I’ve had after, makes him feel like he’s in a good place and his golf is moving in the right direction.”
He continued: “I know the values of him as a person and now he wants to get out on the golf course and show what he’s capable of. We all know that Sergio at his best, he’s one of the best golfers in the world.
“He’s in a good place. He’s got a big smile on his face and he just can’t wait to get out there, and like all of them on this team they are really buzzing about this Ryder Cup coming up and they want to get out and play golf.”
Bjorn refused to be drawn on whether all 12 of his team would play on the opening day, but revealed he had a strong idea of what he wanted his initial pairings to be.
“I think you prepare yourself 80, 90 per cent and then you know there’s a few little bits that can move as the week progresses,” the 47-year-old Dane said.
“There’s a lot of things that can happen with the players and to the players in a week like this.
“In your mind you’re very set on where you want to go with it, and something uncharacteristic has to happen if you’re going to change it, but you’re pretty much set in your mind where it’s all going to go.”
Bjorn also said that although he had consulted respected sports figures for advice he had no plans to follow in the footsteps of predecessors Paul McGinley and Darren Clarke, who brought Sir Alex Ferguson and Paul O’Connell in respectively to speak to the players beforehand.
“You might ask a couple of people what they think about different things, but I’m happy with where I am as a captain and how I can lead these 12 players,” he said.”