The Toffees activated a release clause in Gueye's contract at the Villans, who he joined a year ago from French outfit Lille.
The 26-year-old defensive midfielder featured in all but three of Villa's 38 topflight games last season but was unable to save the club from relegation to the Championship.
Gueye, nevertheless, arrives on Merseyside with quite a reputation after making the second-most interceptions and tackles in Europe's top five leagues, with only N'Golo Kante ahead of him.
"I am very happy to be here at Everton and I am very happy and excited to put on the Blue shirt to start the new season here," Gueye told evertontv.
"Everton is a big team with big players and great fans. The manager told me he is very happy to have me here and that we will have time to talk about football after.
"I have played a season with Aston Villa which was a hard season but I think my style is good for the Premier League. You have to fight every game. All the teams are strong and you have to concentrate all through the game.
"Goodison Park is a very good stadium and the fans are very good, too. They push their team forward and I am excited to play there."
Koeman added of the Senegal international: "Idrissa will provide quality in our squad in the midfield and we want to increase the quality in the team.
"He was one of the players last season with the best record in interceptions and pressing in the midfield. We need this kind of quality and I'm happy to have him joining our club."
