Kubica, who has not taken part in a grand prix for eight years following the horrific rally crash which left him seriously injured, joins Englishman George Russell at the British team in 2019.
The 33-year-old Polish driver has competed in a series of practice sessions for Williams this year and his promotion to their race team for next season was announced in Abu Dhabi, the venue of his last race back in 2010, on Thursday.
Kubica, whose right arm was partially severed in the rally crash in Italy in February 2011, hailed his return to F1 as “one of the greatest achievements” of his life, admitting the road back to the pinnacle of the sport had seemed “almost impossible”.
He said: “Firstly, I would like to thank everyone who has helped me during what was a difficult period of my life over these last few years.
“It has been a challenging journey to make it back to the Formula One grid, but what seemed almost impossible is now beginning to feel possible, as I am excited to be able to say that I will be on the Formula One grid in 2019.
“For sure, it has been a long road to get to this point, but as that challenge now comes to an end with this announcement, a new challenge begins working with Williams on track.
“It will not be easy, but, with hard work and dedication, both George and myself will work together to try and help the team get in better shape to move further up the grid. This year has been tough, but I have learnt a lot, and I’d like to thank (team principal) Sir Frank (Williams) and (deputy team principal) Claire (Williams) for this opportunity.
“Being back on the F1 grid next season will be one of the greatest achievements of my life and I’m sure with hard work and commitment we will be able to help motivate the team to achieve good things together. Thank you again to everyone who has supported me and believed in me.
“I will finally be back on the grid behind the wheel of an F1 car and I cannot wait to get back racing.”
Claire Williams said the team had been “immensely impressed” with Kubica and praised his “strength of character and tenacity to return”.
“During this season his commitment to the team and the work he has put in behind the scenes has been unwavering and he has become an established and much respected member of the Williams team,” she added.
“He has a level of determination that is remarkable to see and he truly embodies the Williams fighting spirit.”
Kubica’s injuries brought a dramatic halt to an F1 career that had already yielded one grand prix victory and seen him hailed as one of the finest talents on the grid.
His slow journey back to F1 began when he returned to rallying before he took part in a series of tests for his former team, Renault, last year.
Kubica then drove for Williams at last year’s post-season test in Abu Dhabi, but the British team opted to take on the Russian rookie Sergey Sirotkin ahead of the Pole.
Kubica was, however, signed to the team as a reserve driver and has been an ever-present at the races this year.
He now replaces Sirotkin and will bring much-needed experience to a team rooted to the foot of the constructors’ championship after one of the worst seasons in their history.
He is also believed to be bringing a substantial boost to Williams’ financial muscle via PKN Orlon, a major Polish oil refiner.
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