Johnson moves to Everton seven months after joining Palace from Tottenham for 35 million pounds, while McNeil heads to Selhurst Park after three years at Everton.
The deal gives both players an opportunity to revive their fortunes after difficult spells last season.
Johnson, 25, made 26 appearances for Palace without scoring, despite previously scoring the winning goal in Tottenham's Europa League final victory last May.
The Wales international, who has 45 caps, said Everton's ambition under David Moyes was a major factor in his decision.
"I immediately wanted to come and be part of it," Johnson told Everton's club media.
"There were a lot of reasons why I was so keen to join - the manager, the players, the direction the team is going in.
“You can see this is a club that wants to go in the right direction, and I'm a player who wants to go in that direction too, so it feels like a really good match.”
Meanwhile, McNeil leaves Everton after making more than 100 appearances since joining from Burnley for 20 million pounds in 2022. He scored 15 goals and provided 18 assists.
He joins a Palace side that has won the FA Cup, Community Shield and Europa Conference League over the past two seasons and will compete in the Europa League this campaign.
"The lads have had some great success over the last two seasons. It's something that I want to be a part of, so I'm really looking forward to getting started," McNeil said.
Interestingly, Everton host Palace on the opening weekend of the Premier League season on 22 August.
