The Pole will drive for Williams Racing in the upcoming 2019 season, joining the British team alongside George Russell.
"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," Kubica said.
"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.
"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."
Kubica was competing in the Ronde di Andora rally championship in 2011 when he lost control of his car at high speed and smashed into a roadside barrier.
The then 26-year-old, considered one of the most exciting prospects in the sport, was trapped for more than an hour before rescue workers managed to free him, allowing him to be airlifted to hospital.
It was later confirmed he had required a partial amputation of his right forearm, while also suffering severe injuries to his right elbow, shoulder and leg.
"Being back on the F1 grid next season will be one of the greatest achievements of my life," Kubica said.
"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."
Formula One career
Just days before the crash, Kubica had been driving for the Renault Formula One team in preseason testing in Valencia and set the fastest time on the final day.
It was the start of his second year with the team, joining in 2010 after four years with BMW which included victory at the 2008 Canadian Grand Prix.
In August of this year, Kubica told Autosport that he has gradually adapted to his injury and now drives "70% left-handed and 30% right."
Kubica returned to rally driving just two years after the crash and competed in various championships all the way through to 2017, when he made his long-awaited return to F1.
His first step back on the ladder was with his former Renault team in 2017, test driving their 2012 car.
Just a month later, he drove his first modern F1 car since the crash, finishing fourth fastest in testing at the Hungaroring after the Hungarian Grand Prix, just 1.4 seconds behind race winner Sebastian Vettel.
Kubica's impressive performances made him a contender for the 2018 Williams seat vacated by the retiring Brazilian Felipe Massa.
The team instead opted Lance Stroll and Sergey Sirotkin and chose to employ Kubica as a reserve driver behind the scenes.
In May this year, he took part in his first F1 race weekend since the final weekend of the 2010 season, driving in a practice session at the Spanish Grand Prix.
But Kubica will complete his remarkable turnaround when he takes to the starting grid for the opening race of the 2019 season, March's Australian Grand Prix.
"All of us at Williams have been immensely impressed at what he has achieved, and it is a great credit to his strength of character and tenacity to return to Formula One," said Claire Williams, deputy team principal.
"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.
"He has a level of determination that is remarkable to see; and he truly embodies the Williams fighting spirit.
"Having the consistency of Robert stepping up into this new role will be an important step for us as we look to fight our way back towards the front of the field."