The announcement ends speculation about Lawson's future.
"I have no doubt that this is the best driver lineup for us, bringing a strong combination of experience and ambition," said team principal Alan Permane in a statement.
Lawson has scored 75 of Racing Bulls' 114 points so far this season, with the team fifth overall. His place was uncertain, however, with 19-year-old Bulgarian junior driver Nikola Tsolov also linked to the seat.
"We’ve had a brilliant season together, and the team has worked very hard to produce a fast car, which I’ve loved driving," said Lawson.
"It feels great to be part of a historic season for the team as we continue our fight for P5 in the Constructors' Championship ... I’m looking forward to carrying this moment forward with Arvid through to 2027; we’re building something super positive, and I’m excited by what we can achieve together.”
Lawson came seventh in Brazil last Sunday, his 15th scoring finish in 20 races, to confirm his status as the best of the midfield drivers. Three of his races were for Red Bull as a stand-in for injured Frenchman Isack Hadjar.
The Kiwi had started last season at Red Bull but lasted only two races before being replaced by Yuki Tsunoda and dropped back to Racing Bulls.
That left the 24-year-old's future in doubt, with the second Red Bull team seen as a stepping stone to the championship-winning main one and a place for bringing on young talent.
Lindblad made his race debut this season as the sole rookie from the start in Australia and has impressed with his results.