The win gives Juventus its 36th Italian league title overall.
The 38-year-old Swede has agreed on a deal until the end of the season with the option to extend the contract for another season, the club announced.
Cristiano Ronaldo played a key role in the winning goal and Juventus beat Fiorentina 2-1 to clinch a record-extending eighth straight Serie A title.
Real Madrid favourite Zinedine Zidane returned for a second spell as coach on Monday with plans to rebuild the Spanish giants who have fallen into crisis since he left in May after winning an unprecedented third straight Champions League.
Atletico Madrid took a huge advantage in their heavyweight Champions League last-16 tie with Juventus, earning a 2-0 home win.
The UEFA Champions League round of 16 will see three England-Germany clashes and a true test of the Premier League v Bundesliga.
Fans watching the Champions League final on a giant screen in San Carlo Square ran in panic when they mistook firecrackers for an explosion.
In an exceptional career in which he keeps rewriting the record books, Ronaldo is the first player in the 25 seasons of the Champions League era to score in three finals.
Real Madrid will be facing a sturdy Juventus defence supported by a formidable attacking unit led by Paulo Dybala. The Argentine, who has drawn inevitable comparisons with Lionel Messi, has scored four goals in 10 European appearances this season.
After beating Atletico Madrid over two legs, Zinedine Zidane's Real Madrid march into their second consecutive Champions League final, this time facing Juventus in Cardiff.
Italian football has been hit by a second racism storm inside a week after Juventus defender Mehdi Benatia was insulted on air during a live, post-match television interview with Italian state broadcaster Rai.
Juventus crowned Serie A champions for fifth season following Napoli's loss to AS Roma
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