"I'm very happy to be signing for AS Monaco, a club with a great history," he told the club's official website. "I'm very pleased to be here and can't wait to start playing.
"A lot of players and friends have said good things to me about the club, the spirit in the squad and the team. When you get the chance to come here, you accept straight away.
"It's the ideal project for me. I'm very happy to be joining a strong squad, with big players who had a brilliant season last year."
Monaco vice-president Vadim Vasilyev added: "We are delighted to welcome Keita Balde to AS Monaco. He is a young forward who already has over 100 appearances in Serie A and also has experience of European competition.
"He's a player we've been monitoring for some time, who has already shown a lot of quality and in whom we have a lot of faith to continue building a strong side this season."
A product of Barcelona's La Masia academy, Keita developed into one of Serie A's most impressive young attackers during his four years in Rome.
The deal, which follows the confirmation of Stevan Jovetic's move from Inter, comes as Kylian Mbappe is expected to finalise a transfer to Ligue 1 rivals Paris Saint-Germain.
Mbappe is expected to join PSG on a year-long loan before moving on a permanent basis for a staggering €180m next year.