Ayew, 26, signed for Swansea on a free transfer from Marseille in June 2015 and scored 12 goals in his first Premier League season.
The 2011 African player of the year was no doubt delighted with the signing to the olympic stadium, after signing a 4 year deal with the London club.
“The club have a lot of ambition and have a great manager,” said Ayew.
“They want to become a bigger club every year and with the new stadium and a new training ground, you can feel they are moving on to another level and I want to be part of this project.”
The £20.5m fee for Ayew eclipses the £15m West Ham paid Liverpool for England striker Andy Carroll in June 2013.
On Monday, the Hammers also completed the transfer of French left-back Arthur Masuaku from Olympiakos in a deal worth a reported £6m.