The Toffees announced the signing on Thursday afternoon, with McNeil departing Turf Moor for Goodison Park for an undisclosed fee, reported to be in the region of £20million.
The 22-year-old scored seven goals in 137 Premier League appearances for the Clarets before leaving following their relegation last season.
McNeil, who started his career at Manchester United before joining the Burnley academy, revealed he is looking forward to working under Lampard.
"It is an amazing feeling to sign," he told evertontv.
"When I heard about Everton's interest I wanted to get it done straight away because of the club and how good the team is.
"I feel playing under a manager like Frank Lampard, he will help me to get my stats up - and that is what I want to do and improve my game.
"Speaking to the manager about what they want going forward, it really excited me and appealed to me. I wanted to be part of it. He knows me as a player, as does (director of football) Kevin Thelwell. I want to work hard and do well for the team and for the fans."
Lampard has called for reinforcements this summer as he looks to avoid the type of relegation dogfight which almost cost Everton their top-flight status last year.
"I have been a big admirer of Dwight for some time," the former Chelsea boss said.
"He has huge talent and is exactly the type of player we want to bring into the squad to help us improve."
McNeil becomes Everton's third summer signing and joins former Burnley team-mate James Tarkowski in the Everton dressing room along with Ruben Vinagre, who has signed on a season-long loan from Sporting Lisbon.