Everton pay Southampton compensation for Dutch boss
Everton have been without a manager since they sacked Roberto Martinez just before the end of the 2015-16 season.
Koeman said Everton is a club with a "great history and real ambition", while chairman Bill Kenwright called the Dutchman his "number one target".
A deal with the former Netherlands international, headhunted by new owner Farhad Moshiri, was agreed earlier in the week and is reported to be worth about £6m a year.
The official announcement was delayed until Koeman returned from holiday.
"Ronald has such a strong track record in the game, instantly commanding respect for what he achieved as a player and for his qualities and accomplishments as a manager," added Kenwright.
"We are really pleased to have secured the man who was our number one target from the moment we set out to appoint a new manager."
Everton will face his old side Southampton in November at St Mary's and in January at Goodison Park.