Sanches was named the best young player at Euro 2016 after helping Portugal to the trophy last summer, earning a big-money move to Bayern from Benfica as a result of his performances.
However, the 20-year-old made just six Bundesliga starts during his time in Germany and was made available for a temporary move away from the Allianz Arena having failed to nail down a regular first-team place in Carlo Ancelotti's side.
Giggs revealed that he scouted Sanches during his time as United's assistant manager under Louis van Gaal and is confident that the midfielder has all the attributes to succeed in the Premier League.
"It didn't quite happen for him last year at Bayern. That can happen; a young player moving country, different language, a big club and a lot of expectation. But he is a talent and the Premier League will suit him because he's an aggressive player," Giggs told PA.
"He can tackle, he can get forward and he's going to a club that play football the right way, so I think he'll be a success. I remember watching him three years ago in Louis's first season and instantly liking him. I thought then that he would suit Premier League football.
"Paul Clement's ties to Bayern and his friendship with Carlo Ancelotti has obviously got a lot to do with him coming to Swansea. But you've got to capitalise on stuff like that. He's a fantastic player and I think he will be one of the most exciting players in the league."
Sanches could make his debut for Swansea when they host Newcastle United on Sunday.