The Spaniard, who won the World Championship in 2005 and 2006, started the race in third position and ended up finishing there behind the two title contenders.
This was Alonso's 98th podium finish and his first since 2014, when he was the runner-up at the Hungarian Grand Prix.
F1's official Twitter page posted a video of the 40-year-old celebrating with Hamilton and Verstappen in Al Daayen, and it's just absolutely wonderful to see!
Prior to the Qatar Grand Prix, Alonso's best finish this year came, funnily enough, at the Hungarian Grand Prix, when he finished in fourth place.
"Honestly, I thought about leading after lap one. I thought with the red tyre, I could have a go on Lewis, but I couldn't. Then with Checo it was very close at the end. But I'm so happy for the team. Also Esteban P5, so a good Sunday."
Alonso is now 10th in the Drivers' Championship with 77 points, while his team Alpine-Renault are fifth in the Constructors' Championship with 137 points.
The Spaniard has had an extraordinary career, during which he cemented his status as one of the all-time greats in the sport. He has garnered a lot of fans over the years and they will be thrilled to see him end up on the podium after seven long years away from it.
Alonso has the sixth-most number of podium finishes in F1 history, and now sits just five behind fifth place Kimi Raikkonen.
With only two races to go, the Spaniard will be eager to put in as good a performance he can to end this year's world championship in the best way possible.
Next up for him is the Saudi Arabian Grand Prix in Jeddah, which will take place in a couple of weeks.News Now - Sport News