The transfer fee and length of contract were not disclosed but Italian media said Inter had paid about six million euros for his services.
Sommer, who is first-choice for his country, arrived in Munich in January to deputise in Manuel Neuer's injury absence for the Bundesliga champions.
"There are children who dream of becoming great strikers. Others, meanwhile, are born to play in goal, and this most certainly applies to Yann Sommer," Inter said in a statement.
"Experience, leadership and commitment: these are all qualities that Sommer is now ready to display in Nerazzurri colours."
Simone Inzaghi's Inter were short of keepers having sold Andre Onana to Manchester United for a reported 51 million euros in July, while Samir Handanovic and Alex Cordaz were released.
Romania's Ionut Radu was loaned out to Premier League side AFC Bournemouth last month.
"We understand and respect Yann Sommer's desire to seek a new challenge at Inter Milan because he wants to play as the number one goalkeeper in the long term," Bayern CEO Jan-Christian Dreesen told the club website.
"(He) helped us out in a complicated situation when Manuel Neuer was seriously injured and we would like to thank him sincerely for his commitment."
Sommer, who joined Bayern from Borussia Moenchengladbach, helped Bayern to their 33rd league title this year.
Before switching to the Bundesliga, Sommer won the Swiss Super League with FC Basel four times in a row from 2010-11.
Sommer has made more than 80 appearances for Switzerland having made his debut in a friendly against Romania in May 2012.
