Barnes scored 13 Premier League goals in 34 games last season but could not prevent Leicester from getting relegated.
The 25-year-old was set to play in the Championship next season but will instead have a taste of Champions League football for the first time in his career following Newcastle's fourth place finish last season.
Barnes has signed a five-year contract to become Newcastle's second summer signing after Sandro Tonali.
He is set to come in as a direct replacement for Allan Saint-Maximin, who is on the cusp of a transfer to the Saudi Pro League.
Barnes came through the Leicester City youth ranks and established himself in the first team in the second half of the 2018/2019 season after spending loan spells at M.K Dons, Barnsley and West Bromwich Albion.
Barnes went on to make 187 appearances for the Foxes, scoring 45 goals and registering 32 assists, winning the FA Cup in 2021.
On his switch to Eddie Howe's side, the Burnley-born winger told Newcastle's website: "I'm delighted.
"It's an amazing club and for me it's a massive opportunity to come and be involved in a successful team that's doing exciting things, so I'm absolutely buzzing to be here.
"I think it's an attacker's dream to come into a team like this; it's high paced, it's physically demanding, but you can see the rewards of that with the chances and the goals scored, so I think I'll certainly suit the style."
Magpies boss Howe added: "Harvey is an exciting talent who I have admired for a long time so I'm delighted to welcome him to Newcastle United.
"He is strong, quick and very good technically, and he showed last season in particular that he has an eye for goal from wide positions.
"He will add a different element to our play and we look forward to working with him as we prepare for the season ahead."
Barnes won his solitary England cap against Wales in October 2020.
