The 39-year-old has been widely reported as being on the brink of taking charge at Inter ever since Alberto Zaccheroni's resignation last month.
Lazio's director general, Giuseppe De Mita, announced the decision to let Mancini go at the end of a shareholders meeting on Tuesday.
"We've resolved all our outstanding issues as regards Roberto Mancini. As far as we're concerned he's released (from his contract). Now he's Inter's problem," De Mita was quoted as saying by Italian press agency Ansa.
Mancini's agent, Giorgio De Giorgis, said he expected his client's move north could happen as early as Wednesday.
"Everything's OK between Lazio and Inter, and Lazio and Mancini," he said.
"Mancini doesn't yet have a formal agreement with Inter and I don't expect his move there to be made official this evening. I believe tomorrow (Wednesday) we'll meet with Inter."
The former Italy international, whose deal with Lazio was not due to expire until 2008, is considered one of the brightest young coaches in Serie A.
Having started out as assistant to Sven Goran Eriksson at Lazio, Mancini took over Fiorentina during the 2000-2001 season, leading them to the Italian Cup in his first season in charge.
He quit the following year as Fiorentina spiralled towards bankruptcy before rejoining Rome-based Lazio in August 2002.
Mancini again had to cope with serious financial problems that forced the departures of players Alessandro Nesta and Hernan Crespo, but guided the club to fourth place in Serie A and the semi-finals of the UEFA Cup in the 2002-03 season.
Last season Lazio won the Italian Cup and finished sixth in Serie A.
At Inter, money is less of an issue, though the pressure of delivering the club's first Serie A title since 1989 has already claimed the jobs of a string of experienced coaches, including former Juve boss Marcello Lippi.
If appointed Inter coach, Mancini would become the 11th man to hold that position since Massimo Moratti bought the club in February 1995.
