The 32-year-old Portuguese international had a year left on his contract with the Spanish club - but after completing a medical has agreed a two-year deal with the Serie A side.
Real spent a then world record $56 million to buy Figo from rivals Barcelona in July 2000 in one of the most controversial transfers in Spanish football history.
Figo becomes the third player to move from Real to Inter during the close season following Argentines Santiago Solari and Walter Samuel as Inter coach Roberto Mancini looks to end their 16-year wait for an Italian title.
The skillful winger will operate in a midfield featuring Argentine internationals Juan Sebastian Veron and Esteban Cambiasso and will be expected to provide the ammunition for Inter's prolific Brazilian striker Adriano.
Despite remaining one of the biggest names in the game Figo will have a point to prove at Inter following a disappointing end to his time in Madrid.
The winger fell out with Real coach Vanderlei Luxemburgo after being consigned to the bench for the latter part of last season and had been given permission to negotiate with other clubs.
Real are reported not to have demanded a fee for the player who had also been linked with Liverpool and Valencia.
Figo began his career at his home club of Sporting Lisbon making his name as part of the golden generation of Portuguese youngsters who won the World under-16 and under-20 championships in 1989 and 1991.
He moved to Spain in 1995 to sign for Barcelona quickly becoming a favourite among the club's fans for his committed and skilful performances on the right wing.
He won seven trophies in a five-year spell at the Catalan club including two league titles two King's Cups and the Cup Winners' Cup.
But Figo was transformed from hero to villain in the eyes of the Nou Camp faithful when he defected to arch-rivals Real in July 2000.
The midfielder viewed as Real's first Galactico signing helped his new club to the league title in his first season and played an important part in their victories in the 2002 European Cup and 2003 Spanish championship.
Now he faces a new and tough challenge as Inter's fans tired of years of domination by rivals AC Milan and Juventus expect him to play a key role in their title challenge.
Figo could make his debut for Inter in the Italian Super Cup against champions Juventus on August 20 -- a week before the start of the Serie A season.