The 55-year-old Dutchman left Hillsborough “by mutual consent” after a run of just one win in 10 games had seen the Owls slump to 18th in the Championship.
Coach Lee Bullen will take charge of the team for Saturday’s visit of Preston North End.
Chairman Dejphon Chansiri said: “I would like to place on record my thanks to Jos for the efforts he has given to Sheffield Wednesday.
“But now is the right time for both parties to move on and I wish him all the very best for the future.”
The Yorkshire Post understands former Huddersfield Town and Hull City manager Steve Bruce is favourite to replace Luhukay.
If talks are successful, Bruce could arrive at Hillsborough after Christmas following a pre-planned family holiday. He would also bring in backroom staff Steve Agnew and Stephen Clemence.
Wednesday fans left a lasting impression on Bruce, who helped Hull beat the Owls at Wembley in the Championship play-off final in 2016.
Afterwards Bruce said: “The Wednesday fans were terrific. I didn’t have a clue what they were singing when bouncing up and down, but they were brilliant.”
His challenge would be to get the club ‘bouncing’ again, but the former Manchester United defender – who started his managerial career across the city at Sheffield United 20 years ago – would inherit an Owls squad low in confidence.
Several high-profile players, including Republic of Ireland goalkeeper Keiren Westwood and defensive midfielder Sam Hutchinson, have been frozen out, and supporters chanted for the manager to be sacked in their last three games.
Chansiri met with the Owls players on Monday to discuss the club’s slump, and 48 hours after supporters at a fans’ forum urged him to axe Luhukay on Wednesday night, the Thai businessman acted on Friday.
Since replacing Carlos Carvalhal – who left the Owls on Christmas Eve last year – on January 5, Luhukay has struggled to adapt to English football.
A veteran of German football, he was in charge for 48 games at Hillsborough, winning 16, drawing 13, and losing 19.
His first game was a 0-0 draw at Bramall Lane in the Steel City derby in January, and while he repeated that feat last month Luhukay was in charge for some shocking defeats, including a 4-0 home collapse to Norwich City.
One of the criticisms aimed at Luhukay has been his failure to stick with a settled team.
Owls captain Tom Lees, speaking before the manager’s exit was confirmed on Friday night, believes the Owls have struggled with their “identity and game plan” this season.
“Any player wants to be playing to get that momentum, it’s difficult to come into a side if you have not been playing for a few weeks,” he said. “But I wouldn’t use that as an excuse. You could swap the personnel and formations round a bit more if you fully all nailed down what you are doing, with an identity and game plan.
“I don’t think we have ever nailed that down. That changing has been the problem, more than players and formations.
“I could show examples of other teams where you know exactly what they are going to do every game, and it doesn’t really matter who is playing. I don’t think we have got that sorted just yet.”
With tough away games to come over Christmas at Middlesbrough and West Brom, Bullen – who was also in temporary charge over the festive period last year – has urged Wednesday fans to get behind the team for Saturday’s visit of Preston.
Sitting just five points above the relegation zone, Wednesday – who have the worst defence in the Championship and have won just six times all season – are desperate for three points.
“I can understand the emotions and the disappointment and the desperation from everybody,” said Bullen. “We are feeling the same. We are all going through the same hurt, but we’re all trying to get to the same end and get this club heading in the right direction.
“All I can ask for is to try and stick by the players as much as they possibly can.”