As anticipated by Motorsport.com, the 2008 Canadian Grand Prix winner will join George Russell at Williams for next year and end an absence on the F1 grid for more than eight years.
Kubica has not been in F1 since the end of the 2010 season, having suffered serious injuries to his right arm in a rally accident in early 2011.
Securing a place as starting driver for 2019 means that Kubica will complete an incredible recovery from the injuries he suffered in that accident, which prevented him from competing for several years.
Kubica, who says he now drives "70%" with his left hand, has not competed in single-seaters since the last of his 76 GPs in F1.
His first sportive activity after the crash was at rallies before returning to race circuits in the Mugello 12-hour GT race in 2016.
Kubica completed a successful test last year with a Renault F1 of 2012, before riding Renault and Williams in 2017 in Hungary and Abu Dhabi respectively.
The deal with Williams means the 33-year-old has secured the place he originally proposed for this season before having to settle for a reserve driver role.
It is also believed that Kubica received a firm offer from Ferrari to take on a development role with the Italian team in 2019.
Robert Kubica, Williams FW41
Photo by: Andrew Hone / LAT Images