The three internationals were presented at an event as Jorge Jesus’ Benfica revolution picks up pace.
Highly-rated Brazil winger Everton, 24, joins from Gremio for a fee of at least €20m.
Germany international Waldschmidt, 24, has cost Benfica around €15m and arrives from Freiburg.
And experienced Belgian defender Vertonghen, 33, joins the Lisbon club on a free transfer after leaving Spurs.
The trio were all coveted by top clubs in Europe but Benfica were able to convince them with an exciting sporting project.
And it is unlikely to end there, with Jorge Jesus still hoping to add more new faces to his squad.
Talks continue over a move for free agent Edinson Cavani, one of Europe’s top marksmen over the past decade.
Benfica finished second in Liga NOS last season, five points behind champions FC Porto.
However, with signings of this calibre, next season could be a much closer title race.