Chelsea's other right-back, Portugal international Paulo Ferreira, signed a five-year deal earlier this season and is unlikely to move on.
United have long been in the hunt for a rightback and assistant coach Carlos Queiroz confirmed their interest earlier in the season, admitting: "He's a very good player and we are keeping an eye on him."
United saw him as a potential successor to Gary Neville but Chelsea have moved swiftly to snap-up the attack-minded defender.
Bosingwa is set to play for Portugal in Euro 2008, but was born in Kinshasa in the Democratic Republic of Congo.
He moved to Seia in central Portugal when he was young and began his career mainly playing in midfield for Boavista, where he made more than 40 appearances.
His performances there caught the eye of former Chelsea boss Jose Mourinho who signed him for Porto in 2003, where he has been first-choice right-back for the last three seasons - ironically replacing Ferreira.
Three years ago, Bosingwa was involved in a serious car accident when his jeep skidded off a motorway and rolled down an embankment before bursting into flames.
He was with four other players at the time, but all survived. However Sandro Luis, a fellow passenger, had to have his left foot amputated as a result of the accident.
