"To love the club is good, to prove it is better," the forward, who had previously refused a pay cut amid the COVID-19 crisis, told a joint news conference with coach Andre Villas-Boas and president Jacques-Henri Eyraud.
His salary for 2021-22 will be 30% less than this season's reported €6 million.
"I went to see the president to make this proposal," added Payet.
Payet, who helped take France to the Euro 2016 final, won the last of his 38 caps in October 2018.
Marseille are under financial pressure, having been fined €3 million this month for breaching a settlement agreement relating to financial fair play (FFP) rules.
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European soccer’s governing body UEFA said it would permanently withhold "15% of the revenue that the club would be entitled to receive from any participation in UEFA club competitions" for the next two seasons.
Eyraud, however, said that "OM is not for sale" amid speculation that former rugby club RC Toulon's owner Mourad Boudjellal may make an offer for the side on behalf of an unnamed businessman.