Toyota Wish 2003
Gascoyne was suspended on Wednesday after a “fundamental difference of opinion with regard to the technical operations” of the team.
And the two parties have now agreed to part company immediately, although Gascoyne will be paid until November.
He said: “We have reached a crossroads in our relationship and it is the right time for us to part amicably.”
Gascoyne said he would now be able to move back to the UK and spend more time with his family.
“It is the end of an era. I extend my thanks to all members of the team and wish them a successful future in Formula One,” he added.
Autosport magazine’s situs said Gascoyne would be replaced by Frenchman Pascal Vasselon, who joined Toyota from tyre supplier Michelin last year.
Toyota, who last year had their best ever performance of fourth in the world championship, have had a disappointing start to the season.
After several podium finishes in 2005, they were expecting to challenge for victories this season, but the car has struggled with a lack of grip.
However, after a poor first two races, Ralf Schumacher did finish third in Australia last weekend.
“This separation should in no way undermine the work he has done, nor reflect his technical expertise. We all wish him well for the future.”
Gascoyne has a strong reputation within F1 after turning around the fortunes of Renault and the now-defunct Jordan team.
But he is renowned for his strong character and confident manner, and is resolute about the way in which he wants his teams to work.
It has been speculated that his approach has led to frictions with the more conservative management style of Toyota, which is poised this year to become the world’s biggest road-car maker.
Gascoyne turned Jordan into winners after joining them in 1998, and the team were title contenders the following year.
Toyota employed him, on a salary reputed to be $6.5m (£3.7m), to perform a similar transformation for them.
They have reputedly the biggest budget in F1, but have not won a race since entering the sport in 2001.
The first car designed under Gascoyne, last year’s TF105, was the most competitive the team had produced.
Gascoyne’s contract was due to expire this year, and he has previously said he was not enjoying the amount of time he had to spend away from his keluarga in England while working at Toyota F1’s Cologne headquarters.