Carolyn Fairbairn, director-general of the CBI, told the Yorkshire Post that MPs should vote for Mrs May's deal tonight as it delivers a transition period and tariff-free access to the EU.
Talking about the dangers of a no-deal Brexit, Ms Fairbairn said: "We can see absolutely no advantages at all of WTO rules and that comes directly from our members. WTO terms are the most rudimentary trade terms in the entire world. There is no country in the world that trades on WTO terms alone. We would be joining a club of one.
"The frictions that would be created in our trading system are unconscionable really. 90 per cent of our exports would face tariffs. We would be introducing customs checks at borders, five times the volume of customs checks compared with now. Our systems are not ready.
"So WTO terms - I've used the term reckless for people who have tried to say that it would be easy. There is not a shred of evidence from anybody that this would be anything other than an extraordinarily challenging thing for the majority of British businesses."
She said that Mrs May's deal will deliver a transition period and removes no-deal from the table.
"That is of remarkable importance - a clarification for businesses," said Ms Fairbairn.
"It also delivers tariff-free access. People sometimes lose sight of that, that actually the future declaration is absolutely clear that even in the long term there will be no tariffs. That is a very important thing.
"And the third thing that it offers is a pathway to a decent trade deal. We've been really clear that it's not perfect. It doesn't bring all the clarity that businesses wanted, but it brings something they can work with and move on from.
"So yes we are hopeful that MPs will recognise that the alternatives of ongoing uncertainty, the Brexit roundabout, the frustration, is just not worth it."
When asked if it is possible that the UK and EU could thrash out a deal in just 21 months, she said: "One of the things we've learned over the last two years is how quickly both the European Union and the UK can move when they have to. And the power of the deadline, for example the revocation of the Article 50 agreement reached by the ECJ. They reached it in record time - one week - whereas it normally takes six months. The agreement that's been reached in the last few days, which is actually quite complex, has been done in two or three days."
She said that the trade deal between the UK and the EU would be very unusual in that the two sides are starting from complete alignment and the UK has an ambition to remain close to the European Union.
"It's not like Canada and the European Union, which started from here and were trying to move to there," she said.
"We're starting from here and we're moving a little bit apart. So I think the view of business, and it is something that I'll be saying pretty strongly, is stick to that deadline. We don't want this dragging on interminably. That is the way you'll avoid any kind of backstop needing to be triggered and let's just get on with it."