The stocky 23-year-old, who joined Bayern in 2012, will undergo a medical in Italy on Friday before signing the deal, Bayern said.
Bayern also said they had loaned out talented 19-year-old midfielder Pierre Hojbjerg to Augsburg until the end of the season to gain match practice while also extending the Danish international's contract by two years to 2018.
Despite some good spells Shaqiri has failed to hold down a regular starting spot under coach Pep Guardiola and had repeatedly hinted at leaving in the transfer window.
He made three starts in 17 league games this season and has scored a total of 11 league goals in 52 Bundesliga appearances for the Bavarians.
"Inter and FC Bayern agree terms for Shaqiri. Just the paperwork to be signed," the club said on Twitter.
There were no details regarding the length of his contract with the 2010 Champions League winners, who have also signed Germany international Lukas Podolski in recent days.
Hojbjerg, Bayern's youngest ever Bundesliga player, making his debut at age 17 in 2013, has played only 17 league games since joining from Brondby in 2012, including eight in the current campaign.
(Reporting by Karolos Grohmann; editing by Justin Palmer)
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