The 24-year-old came through the Chelsea youth system and scored 27 goals in 129 Premier League appearances for the club since making his senior debut in 2019.
Man Utd have reportedly agreed a £55 million transfer for Mount.
"Given the speculation over the last six months this may not come as a surprise to you, but it doesn't make it any easier to tell you that I've made the decision to leave Chelsea," Mount said in a farewell message to Chelsea fans on Instagram.
"I feel you deserve more than just a written statement, so I wanted to tell you directly how grateful I've been for all of your support over the last 18 years.
"I know some of you won't be happy with my decision, but it's what's right for me at this moment in my career.
"I joined Chelsea when I was six years old and we've been through a lot together."
Mount won the 2021 Champions League title with Chelsea, setting up Kai Havertz's winning goal in the 1-0 victory over Manchester City in the final.
He has scored five times in 36 appearances for England.
But Mount struggled for form and fitness in a disappointing 2022-23 campaign, netting just three times in 35 matches in all competitions.
Completing a deal for Mount would bolster the options for United boss Erik ten Hag in midfield.
Chelsea, under new manager Mauricio Pochettino, are seeking to reduce their bloated squad after a huge spending spree over the past year.
The west London club have sold goalkeeper Edouard Mendy and defender Kalidou Koulibaly to the Saudi Pro League and midfielder Mateo Kovacic has left to join Premier League champions Manchester City.
Midfielder N'Golo Kante also left Stamford Bridge for Saudi champions Al Ittihad on a free transfer.
