The 25-year-old will also drive in a rookie test day, the former world champions announced at a news conference in Tel Aviv, and be involved in simulator sessions at the Grove factory.
"This is a landmark for motorsport in Israel," Nissany said in a statement.
Williams finished last in 2019 with just one point from 21 races and have lost some prominent sponsors, with Unilever switching to McLaren and Polish oil company PKN ORLEN following Robert Kubica to Alfa Romeo.
The proudly independent team, winners of nine constructors' titles and seven drivers' crowns between 1980 and 1997, have tumbled down the standings and scored just eight points from the last two seasons.
Their last race win was in 2012.
They now have the least experienced driver line-up with Canadian Nicholas Latifi, the only rookie on the grid, alongside highly-rated Mercedes-backed youngster George Russell who debuted last year.
Latifi has brought several sponsors with him and the Nissany deal will see the Israel Start-Up logo appear on the car on those grand prix weekends when he is driving.
Nissany competed in Formula Two in 2018, finishing 22nd and scoring one point from 20 races, and will race again in the series this year.
He tested for Williams in Abu Dhabi last December, posting the slowest time of the session with a lap more than three and a half seconds slower than Latifi.
His father Chanoch is the only other Israeli to have taken part in a Formula One grand prix weekend, having driven a Friday practice session with now-defunct Minardi in Hungary in 2005.
Williams also have Britain's Dan Ticktum, a two-times Macau F3 winner, and W Series champion Jamie Chadwick as development drivers. (Reporting by Alan Baldwin, editing by Christian Radnedge)