He expressed his excitement about joining the Merseyside club.
Barcelona were close but failed to score four goals and level the game on aggregate, as Atletico won 4-3.
Barça took the lead inside the opening minutes through a powerful solo effort from Robert Lewandowski into the bottom corner beyond Unai Simón.
Manchester United will face Tottenham, who defeated Bodo/Glimt on a 5-1 aggregate scoreline, in the final at the San Mames Stadium in Bilbao on May 21.
Manchester United and Tottenham Hotspur have taken big steps toward the Europa League final.
Mr Partey will remain in London to recover an injury that has kept him out of action for some time.
“The player will undergo surgery in the coming days,” the club said.
The semi-final represents a chance for Real Madrid to get revenge for their 3-1 loss two weeks ago in the Spanish Super Cup against Barcelona.
The club said further tests would be carried out on Wednesday to ascertain the full extent of the injury.
Born to Ghanaian parents who emigrated to Spain, Williams played for Spain Under 21 team and made one appearance for Spanish national team.
