Dutch driver Giedo van der Garde has dropped his legal action against Sauber, allowing them to race in the season-opening Australian Grand Prix.
A court backed Van der Garde's claim he had a valid contract and Sauber risked having its assets seized and team principal Monisha Kaltenborn arrested.
Van der Garde said he had given up his rights "with respect to the interests of motorsport and F1 in particular".
Sauber will now race this weekend with Marcus Ericsson and Felipe Nasr.
Van der Garde, 29, added in statement that the decision had been "very difficult".
He said: "My management will continue talks with Sauber early next week to find a mutually acceptable solution for the current situation that has now arisen.
"I am confident such a solution will be found and I will inform the media once done."
In farcical scenes on Friday, Van der Garde had appeared in the Sauber garage wearing his race overalls and had a seat made - although the team never had any intention of allowing him to race.
"Sauber can confirm it has been able to agree with Giedo Van der Garde that he refrains from driving in the Australian Grand Prix so it can keep its original planning," said a Sauber statement.
"The Sauber F1 Team, Mr Van der Garde and his management will continue to have constructive talks in order to find a mutually acceptable solution."
Van der Garde won the initial case and a subsequent appeal, but his lawyers launched a contempt of court action against Sauber, forcing the team to comply with the order.
A Supreme Court judge agreed to adjourn the case on Friday but urged both parties to try and work out a solution.
Van der Garde signed a contract to race for Sauber in 2015 last summer, paying the team a reputed fee of eight million euros (£5.7m).
However, Sauber, who have been in financial trouble for some time, later signed contracts with Nasr and Ericsson, who are between them reputed to be bringing 40m euros (£28.5m) to the team.