Former Atlético Madrid defender Manquillo has signed a four-year deal, having become an increasingly important part of Steve Bruce's team this term.
And Carroll, who rejoined his boyhood club last summer, has penned a one-year extension.
Meanwhile, Matty Longstaff - whose existing deal was also due to expire at the end of the month - has agreed a short-term contract which will run until the end of the current season, which has been prolonged due to the coronavirus outbreak.
Following discussions with the club's three on-loan players and their parent clubs, the Magpies can also confirm that Nabil Bentaleb and Danny Rose have extended their loan agreements from Schalke 04 and Tottenham Hotspur respectively until the revised end of the season.
Valentino Lazaro and Inter Milan have agreed in principle to extend his loan until the end of the current season and the documentation to formalise this is expected to be signed in the coming days.
It means all three players will be available for United's final seven league matches and remaining Emirates FA Cup ties.
Steve Bruce said: "I'm really pleased that we have been able to put these extensions in place and I'd like to thank the players for committing themselves to the club with some very important games left to play.
"We have been proactive in trying to reach these agreements and they will give us the best chance of finishing the season as strongly as possible.
"I'm delighted Javier Manquillo and Andy Carroll have extended their contracts longer term.
"They have both made important contributions this season and I'm really pleased we can continue to call on them beyond the summer."
However, Rob Elliot, Jack Colback and Jamie Sterry will leave the club when their current contracts expire at the end of this month.
Long-serving goalkeeper Elliot, 34, joined Newcastle from Charlton in 2011. He made 68 appearances during his nine-year spell, playing in the Europa League in 2012/13 and winning a Sky Bet Championship winners medal in 2016/17. Elliot was named as the club's player of the season in 2015/16, but hasn't played for the Magpies since December 2017.
Colback, 30, was a free transfer arrival from Sunderland in the summer of 2014 and was a regular first team player in his first three seasons. The Killingworth-born midfielder made 102 appearances, scoring five goals, but hasn't featured for the Magpies for more than three years and has has two successful loan spells with Nottingham Forest during that time.
Sterry, a product of the Little Benton Academy, was handed his first team debut on the final day of the 2015/16 season as United beat Tottenham 5-1. He made 12 appearances in all competitions as well as spending time on loan with Coventry City and Crewe Alexandra.
Also departing at the end of the month will be Luke Charman, Víctor Fernández, Liam Gibson and Nathan Harker.
Steve Bruce said: "Many of the players leaving us have been with the club for a long time and, both personally and on behalf of the club, I'd like to thank them.
"I'm sure supporters will join me in appreciating their efforts over the years and we wish them the very best with the next steps in their careers."
