The Toffees confirmed the deal on Tuesday after agreeing a £5million compensation package with Southampton.
“We are really pleased to have secured the man who was our No.1 target from the moment we set out to appoint a new manager,” Everton chairman Bill Kenwright said.
“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.
“The hopes and aspirations that we all have as Evertonians are with him, as is our total support at board, shareholder and fan level.”
Koeman leaves Southampton after two impressive years in charge of the south coast club.
Having replaced Mauricio Pochettino in 2014, Koeman guided the Saints to seventh and sixth-placed finishes in the Premier League.
The former Ajax and Feyenoord manager had just 12 months to run on his contract and had previously played down talk of a new deal.
Although his release from Southampton was secured over a week ago, the completion of the deal was held up by the fact the Dutchman was on holiday.
However, on his return the deal was quickly wrapped up, with the 53-year-old’s brother and assistant manager Erwin and fitness coach Jan Kluitenberg also following him to Goodison Park.
Koeman said: “I am very excited to be Everton manager. I believe in the club, in the team, in the fans and in our ability to achieve things in the future.
“Everton is a club with a great history and real ambition and it is a proud feeling for me to be part of what we want to go and do, together with the chairman and Farhad Moshiri.
“I am looking forward to meeting everyone at the club and to preparing for a big season in the Premier League.”
Southampton started their search for a replacement as soon as the £5m compensation deal had been thrashed out with Everton.
The Saints confirmed on Tuesday they had accepted Koeman’s resignation and were now targeting his successor.
“The search has already begun for the right appointment who can take the club to the next level and build on our track record of recent success, which culminated in a sixth-place finish in last season’s Premier League, as well as qualification for the group stages of the Europa League,” Southampton said in a statement.
“Our focus now is to build on our long-term plan, and work with a new management team who share both the club’s and our supporters’ values and ambitions.”