The 26-year-old left-back, who can also operate as a wing-back, is the Magpies' fourth arrival of the January transfer window and follows the permanent additions of Kieran Trippier, Chris Wood and Bruno Guimarães at St. James' Park.
Targett - who will wear squad number 13 - adds Premier League experience to Eddie Howe's defensive options having made more than 100 top-flight appearances with Southampton and Aston Villa.
Speaking after completing his loan move to United, Targett said: "I'm delighted to be here. I can't wait to get going and meet all the fans and hopefully we can have a successful end to the season.
"My family have friends here and they've always said it's a football-mad city, so to experience it and be part of it - I'm really looking forward to it."
Eddie Howe said: "We have gone into this transfer window with a plan to add strong competition in specific areas of the team and Matt will be a fantastic option for us on the left.
"He has important Premier League experience and know-how at this level, so I'm really pleased we've been able to add him to the squad."
Born in Eastleigh in Hampshire, Targett began his career at nearby Southampton.
After coming through the club's academy system, he made 63 appearances in all competitions for the Saints and spent time with Fulham on loan during the 2017/18 season as the Cottagers achieved promotion to the Premier League.
Targett joined Aston Villa in July 2019 and was an ever-present in the Premier League last season as Villa finished 11th - one place above the Magpies.