Kubica, the 33-year-old Polish driver who has not competed in F1 for more than seven years following a life-threatening rally crash in 2010, tested for the British team in the hope of racing again.
But the team, based in Oxfordshire and a winner of 16 combined championships, have instead opted for Sirotkin, the 22-year-old Russian, who has competed in a number of practice sessions, but is yet to make his full grand prix debut.
It is understood, however, that Kubica is still in contention for a reserve seat with the British outfit this year.
Sirotkin, who will bring an estimated £13million in backing to Williams, will join forces with Canadian teenager Lance Stroll to form the most inexperienced line-up on the grid.
Stroll, 19, will enter only his second season while Sirotkin replaces Felipe Massa who retired for a second time at the end of last year.
“To say I’m happy and proud to join such a famous team like Williams is an understatement,” Sirotkin said. “It took a huge amount of work to get where I am, and I’m really happy and thankful to everyone involved.
“The result of our combined efforts has helped me achieve my dream, and rest assured the team can rely on me to deliver my best.”
Sirotkin, who has twice finished third in the GP2 championship, the feeder series to Formula One, has been a test driver for Sauber and Renault.
He tested against Kubica, in what was seen as a straight shoot-out for the seat alongside Stroll, following the Abu Dhabi Grand Prix in November. He is the third Russian to land a full-time seat in Formula One.
Deputy team principal Claire Williams added: “We have taken our time to evaluate all the available options, and I’m confident Lance and Sergey can deliver the best results for the team.
“The Williams philosophy has always been to promote and develop young talent and Sergey fits right into that ethos.
“Lance has had a record-breaking debut season, and with a year now under his belt, he will be ready to hit the ground running in 2018.
“We have a talented driver line-up for 2018, that we are confident will deliver some exciting results for the team.”
The announcement by Williams is the final piece in the driver jigsaw for this year’s campaign which gets under way in Melbourne on March 25.
Provided by Press Association Sport
When Lewis Hamilton said at the end of the Formula One season that he, Fernando Alonso, Max Verstappen, and Sebastian Vettel would be the drivers to beat next year, observers quickly noticed a name he'd forgotten to mention.
Verstappen's boss, Red Bull team principal Christian Horner was quick to set the record straight, saying Daniel Ricciardo is definitely a part of that elite group - and the Australian's performances this season and over his career make it likely that Hamilton made an honest mistake in not including him.
Of course, there will be no future errors from the four-time world champion if Ricciardo partners up with the Brit at Mercedes as rumours over the Aussie's long-term future persist.
The 28-year-old is out of contract with Red Bull at the conclusion of next season and is reportedly assessing his options as he weighs up the best avenue for silverware with Mercedes and Ferrari both possible destinations.
But for his part, the ever-smiling Ricciardo is focusing on next season, when he'll have plenty of chances to show he belongs.
Alfa Romeo are returning to Formula One after a 30-year absence as backers of Sauber next year, the iconic Italian marque announced on Wednesday.
The Ferrari-powered team will be known as Alfa Romeo Sauber.
Ferrari chairman Sergio Marchionne, CEO of the Milan-based manufacturer’s company Fiat Chrysler Automobiles, said in a statement that Alfa was “determined to begin writing an exciting new chapter in its unique, legendary sporting history”.
Pascal Picci, Chairman of Swiss-based Sauber Holding AG, added: “We are very pleased to welcome Alfa Romeo to the Sauber F1 Team.
“Alfa Romeo has a long history of success in Grand Prix racing, and we are very proud that this internationally renowned company has chosen to work with us for its return to the pinnacle of motorsport.”
Alfa Romeo won the inaugural F1 championship with Nino Farina in 1950, and followed up with legendary Argentinian Juan Manuel Fangio winning the 1951 title.
They then served as engine supplier for several teams from 1961 until 1979, before returning with a works team from 1979 to 1985, when they pulled out of F1.
Sauber have yet to finalise their drivers line-up for next season, with Ferrari’s junior drivers Charles Leclerc and Antonio Giovinazzi believed to be in the frame to replace Marcus Ericsson and Pascal Wehrlein.