The first leg of the last-16 match will still take place behind closed doors, which is in line with the Greek government's temporary suspension of spectators attending sporting events.
Wolves called on UEFA to postpone the match after owner Evangelos Marinakis revealed that he had been diagnosed with Covid-19.
All of Olympiacos' players, coaching staff and board members were tested for the virus yesterday and the club has now confirmed that all the tests have come back negative.
Wolves issued a statement late Tuesday night expressing their disappointment in the decision, but confirmed they will fulfil the fixture.
Our position is that the trip poses unnecessary risks to our players, staff, supporters and the families of all who travel, at such critical and uncertain times.
Our concern is also for our opponents, whose players and staff have today been tested, and will now be expected to play their part in an important fixture, under the difficult and challenging circumstances of their owner suffering with the virus.
There is also disappointment that the match will be played without home and away supporters, as that is part of what makes European competition so special, as well as the fact our fans have already contended with similar obstacles on our Europa League journey already this season.
We believe that there are some things that are more important than football, and that the good health of our pack and the general public is one of them. However, we respect the decision of UEFA and the integrity of the competition, and we will travel tomorrow to Greece to play the fixture.
We hope that our request to UEFA, and our acceptance of their decision, can act as the catalyst for them to consider alternative options moving forwards, as this will not be the last fixture to be affected by coronavirus.
Wolves will now fly to Athens on Wednesday afternoon following training at Compton Park.
It comes as Spanish side Getafe said they would refuse to travel to virus hotspot northern Italy to play Inter Milan in their Europa League tie, also scheduled for Thursday.
Asking UEFA to “find an alternative to playing in Milan”, club president Angel Torres told Spanish radio station Onda Cero that Getafe would forfeit the tie if a different venue was not found.
Meanwhile a Premier League game has been postponed due to the virus for the first time, with the Olympiacos owner again involved.
Mr Marinakis, who also owns Nottingham Forest, met Arsenal staff and players during the February 27 Europa League tie at the Emirates Stadium.
As a result the Premier League issued a statement in the early hours of Wednesday confirming that Man City's planned home match against Arsenal on Wednesday evening had been called off.
The statement said: “Thirteen days ago, Olympiakos played at the Emirates Stadium in the Europa League and Mr Marinakis, the Greek club’s owner, met with several Arsenal squad members and staff.
“Following medical advice, Arsenal FC and Manchester City FC consider it is necessary to postpone their fixture due to be played this evening to give time to fully assess the situation."
Despite Marinakis' Forest involvement, the English Football League insists there are no immediate plans to postpone any fixtures.
The Wolves-Olympiacos match is one of many European ties that will take place without spectators.
Manchester United’s Europa League last-16 first leg at Austrian side LASK on Thursday, the second leg of Chelsea’s Champions League last-16 clash away to Bayern Munich next Wednesday and Rangers' second leg at Bayer Leverkusen next Tuesday are among them.
England’s friendly against Italy at Wembley on March 27 is set to go ahead as normal, but Italy’s match against Germany in Nuremberg four days later will be played behind closed doors.