The 60-year-old will have the final say on team selection as he works alongside interim manager Alan Curtis until the end of the season, Swansea said in a statement on their website (www.swanseacity.net).
One of Italy's best known coaches, Guidolin led unfashionable Udinese to third place in Italy's Serie A, the club's highest finish, and has helped Parma, Palermo and Vicenza win promotion.
A former midfielder, Guidolin coached Vicenza from Serie B to Serie A, won the Italian Cup with them in 1997 and lost a UEFA Cup Winners' Cup semi-final against Chelsea in 1998.
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Swansea, playing at home to Watford later on Monday, are 18th in the 20-team Premier League and in the relegation zone.
The only Welsh club in the top flight fired manager Garry Monk in December after 22 months in charge, with the Swans reeling from a run of one win in 11 league games.
Swansea chairman Huw Jenkins said Guidolin's experience would be a huge asset to the club.
"Although we recently appointed Alan Curtis as manager until the end of the campaign, he was aware and comfortable with the fact that we were still looking to bring someone in to assist if we found the right person," he said.
"We believe we have found that person in Francesco."
Jenkins highlighted Guidolin's success in taking on much bigger Italian clubs on a relatively small budget and motivating the players to beat the best.
"It is similar to what this football club is trying to do in the Premier League," he said.
"He also has a wealth of knowledge of players throughout Europe which will be a big boost on our recruitment side; something we have been reviewing in a lot more depth over the last few months."
Swansea said both parties had agreed to review the position at the end of the season with the option of extending Guidolin's contract.
(Reporting by Alan Baldwin, editing by Justin Palmer)
