City started their title defence by coming from behind to beat Red Star Belgrade 3-1 at home.
Suarez remains the only Spanish-born men's footballer to have won the Ballon d'Or.
The 32-year-old has a contract until June 2025 with an option for a further year, while the Spanish champions also said they had included a buyout clause of 400 million euros ($435.72 million).
Gundogan will leave City after captaining the English club to the Premier League, FA Cup and Champions League last season, ending a successful seven-year stint in England where he won 14 trophies, including five league titles.
Puyol played alongside Guardiola for Barcelona and was captain of the Barca team managed by him a few years later, winning the Champions League in 2008-09 and 2010-11.
The move is also a big win for MLS, which welcomed Messi while adding that work remained to finalise the details of the formal agreement.
Barcelona won 27th Laliga soccer title with 4-2 win over Espanyol
Alves had previously denied any sexual encounter with the woman who filed a complaint in January about an alleged sexual assault in a restroom at an exclusive Barcelona nightclub.
Real will fancy their chances of winning the trophy for a 20th time when they face Osasuna in the final after they beat Athletic Bilbao 2-1 on aggregate on Tuesday.
Barca were the better side and earned a well deserved win against a Real Madrid side that at times seemed resigned to their fate.