The Icelandic midfielder, a key inspiration behind his country's surprise run to the last eight of the European Championship in France in 2016, cost a reported 45 million pounds from Swansea City.
"I'm maybe not ready to play 90," he told a news conference on Friday, despite "training well" over the last 5-6 weeks.
Manager Ronald Koeman said he had wanted to snap up the Icelander for a while. "He was, from the start of last season, a long time on my list."
Sigurdsson, a free-kick specialist, was directly involved in 21 Premier League goals last season and covered 433 km (269 miles) in his 38 league games, the greatest distance of any player.
His Swansea side took four points off Everton, but he said of the club where he was on one occasion a young ballboy: "Everton is a big club, an old club in England with good history. They have always been a tough club to play against, so I'm looking forward to not playing Everton this season!"
He said the transfer fee - a record for Everton - did not concern him. "It's not up to me, how much the club pays for me. I put pressure on myself to play well."
(Reporting by Steve Tongue; Editing by Mark Trevelyan)
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