The Serie A club have paid a reported fee of €22 million (£20m/$25m) to sign the 23-year-old, who had also been linked with Arsenal.
The winger has signed a four-year contract with the Serie A side after completing medical checks in Milan.
An Austria international since 2014, Lazaro joined Hertha two years ago after five seasons with Red Bull Salzburg, signing for a reported €6.5m fee.
He made 31 Bundesliga appearances in 2018-19, all starts, scoring three times and providing six assists, which followed a debut season which saw him find the net twice and chip in with five assists.
Lazaro's versatility and success winning trophies in Austria were big factors in Inter's interest in the winger, according to a statement released by the club.
"Lazaro knows how to win," Inter said in a statement announcing the transfer. "He plays mostly on the right flank but is versatile and used to playing in different roles.
"Like many greats of the game, he developed at a young age by playing on the streets, giving him a great base in terms of skill and tactical selflessness."
11 - Valentino #Lazaro has provided 11 Bundesliga assists since November 2017, less only than Jadon Sancho (18), James Rodriguez (13) e Daniel Caligiuri (12) among the midfielders over the same period. Vivacious. pic.twitter.com/jPHyt60Kzs— OptaPaolo (@OptaPaolo) June 27, 2019
Lazaro becomes the latest player to join Antonio Conte's side, with Inter announcing the capture of former Atletico Madrid defender Diego Godin on free transfer earlier on Monday, completing a signing of the Uruguay international that had been long rumoured.
Inter also remain reportedly in the mix for Manchester United striker Romelu Lukaku, while questions continue to surround the future of their former captain, Mauro Icardi and whether he will remain at San Siro.
The club are aiming to build upon a second straight fourth-place finish last season, and will be looking to their new additions and title-winning head coach to springboard them closer to reigning champions Juventus.