Griffin, 23, has agreed a two-year contract with the Aviva Premiership club.
He has made more than 60 appearances for Connacht, and was part of the Emerging Ireland squad that contested the inaugural Tbilsi Cup in Georgia last year.
"Eoin is an exciting, young Irish talent," London Irish rugby director Brian Smith said.
"He is a big, physical centre with great feet and distribution skills, so he will fit in well with the style of rugby we play.
"The form of our centres this season has been superb, so competition for places next season will be fierce, which is what every coach is after."