In an announcement on Saturday (AEST), Benfica revealed the three additions to coach Jorge Jesus's squad.
Vertonghen, who will wear the number five shirt, arrives as a free agent after the experienced Belgium defender left Tottenham Hotspur at the end of the 2019-2020 Premier League season.
Meanwhile, Everton, who was also linked with the English club of the same name, has joined for an undisclosed fee from Gremio.
The 24-year-old winger has made 14 appearances for Brazil, scoring three goals.
Waldschmidt arrives from Bundesliga club Freiburg, having netted seven league goals to help his former side finish eighth in 2019-2020.
A three-time Germany international, Waldschmidt will wear the number 10 jersey.
Benfica finished second in Portugal's Primeira Liga last term, five points behind champion Porto.