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Kubica made a sensational return to F1 with Williams, seven years after partially severing his right arm in a crash at the Rally of Andorra in 2011.
The Pole initially returned as a test driver in 2017 and then reserve driver for the 2018 season before making his full return on race weekends this year.
However, the 34-year-old has grown frustrated with Williams' inability to compete.
"This season has been very tough from a performance point of view, but also been very demanding," Kubica, who won his sole Formula One race at the 2008 Canadian Grand Prix for BMW Sauber, told reporters on Thursday ahead of the Singapore Grand Prix.
"Being back in F1 after such a long time is not easy, especially when you are in a difficult situation as we are."
The Pole has taken Williams' sole point of the 2019 season after 14 races as they languish at the bottom of the constructors' championship.
"I would like to thank the team for the last two years and for helping make my comeback to the Formula One grid possible," he said.
"But I feel that the time is now right for me to move on to the next chapter in my career."
Kubica has not ruled out continuing in Formula One but told the BBC it would not come "at any cost."
"I have to do what will bring me back a bit of joy of racing," he said.
"I am looking forward to the next year and looking for different opportunities," added Kubica, who raced in Formula One from 2006-10 until a rallying accident in February 2011 looked to have finished his career as a race driver.
"In order to evaluate other opportunities I have taken the decision that I will not continue more with Williams, so I will stop at the end of the year with the team.
"This opens opportunities for me in the future in different scenarios. Now I will evaluate what is possible."
Kubica's team mate George Russell has already been confirmed for the team for 2020, where he is likely to be joined by current reserve driver Nicholas Latifi of Canada.
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