The Spaniard's extension, announced on Tuesday, means the sport's oldest active driver will compete at least past his 46th birthday next July.
Alonso, who has started a record 440 races since his debut in 2001 and won 32 of them, told Spain's AS sports daily that he could go on for longer.
"I don't think this will be my last year in Formula One. That's how I see it... I have more experience now and I get organised better. I think I can continue for several years," said the former McLaren and Ferrari driver, who recently became a father for the first time.
'Racing is my life'
Stroll, son of team owner Lawrence Stroll, will continue to partner Alonso for the fifth year in a row.
"I took my time to make this decision, but racing is my life, my passion, and I know I still have the speed and determination to compete at the highest level," Alonso said in a team statement.
"I’m committed for the long term with this team and to helping us succeed. I truly believe in what we are building: we have strong leadership, incredible people, partners and facilities."
Alonso, who won his titles with Renault in 2005 and 2006, joined Aston Martin in 2023 and has taken eight podiums and two second-place finishes with them.
This season has been a struggle, however, with the Silverstone-based team having an uncompetitive car and Honda power unit. They have scored just three points in 15 rounds, all from Alonso, and are 10th of 11.
Alonso has made clear he does not like the current crop of cars and hybrid power units, which need to be driven in a different way with energy management more to the fore, but has kept his faith in top designer and principal Adrian Newey.
He told AS that Aston Martin felt like family: "I'm going to be with Aston Martin for a long time; we'll see in what position. At the wheel or away from it, we'll decide that later."
The Spaniard had been evaluating his position, saying in August that he would consider other positions at the team if they saw greater value in that, but he also had other challenges in mind such as the Dakar Rally or to have another go at the Indianapolis 500.
"Age is not a problem. It's just the motivation, the fun, what remains to be achieved," he said.
"With my family, with my son, priorities keep changing," he told AS. "The important things are what happen at home, having good health, happiness, family balance. It's much more important than a seventh place. I was aware of that before, and I still am now."
Lawrence Stroll said having two experienced drivers was of great value to a team with title ambitions.
"We are here to win, and whilst our short-term focus remains on improving performance, I believe we have the world-class talent we need to achieve our long-term objectives,” said the Canadian, whose son has been at Aston Martin since 2019 but has yet to win a race.