Williams development driver Wolff has prior experience of F1 machinery, having tested for the team at Silverstone in 2013, but she will get her first taste of a 2014 car when she takes over the FW36 from Felipe Massa for the second day in Spain.
Wolff's test will also be used as preparation for her Grand Prix weekend debut on home soil at Silverstone in July. She will run in FP1 at the British circuit, and again in the corresponding session two weeks later in Germany.
McLaren reserve Vandoorne, meanwhile, will make his F1 debut on Wednesday at the Circuit de Barcelona-Catalunya, taking over the MP4-29 from 2009 world champion Jenson Button.
The Belgian, 22, was narrowly beaten to last year's Formula Renault 3.5 crown by Kevin Magnussen, who was subsequently promoted to partner Button for McLaren's 2014 campaign. Vandoorne instead switched into GP2 and won at the first time of asking in Bahrain last month.
While all teams plan to run race drivers on at least one day, another five - Red Bull, Lotus, Sauber, Force India and Caterham - will also use their respective test and reserve drivers.
Sebastien Buemi makes his first official F1 test appearance since 2011, driving for Red Bull on Tuesday before handing over to four-time world champion Sebastian Vettel. Buemi currently leads the World Endurance Championship after helping Toyota to two victories from 2014's opening two rounds.
Charles Pic, meanwhile, will get his first run for Lotus, also driving on the first day before passing the E22 to Pastor Maldonado. Frenchman Pic became Lotus's third driver for 2014 after losing his full-time Caterham drive at the end of 2013.
Pic's former team mate, Giedo van der Garde, will be the final non-regular on Tuesday, driving for Sauber before Esteban Gutierrez comes in for day two. The Dutchman has already tested for the Swiss squad on three Grand Prix weekends, and drove on the second day of the first in-season test in Bahrain in April.
On Wednesday Daniel Juncadella will test for Force India - taking over from Nico Hulkenberg - while Robin Frijns will make his fifth outing for Caterham, where Kamui Kobayashi will drive on the first day.
Mercedes, Toro Rosso and Marussia will split their 2014 race drivers across the two days, while Ferrari are yet to confirm their planned line-up. Mercedes are also expected to test a modified exhaust, designed to enhance the noise produced by the quieter 2014 turbo power units.
As well as providing teams with an opportunity to give their reserve drivers seat time, the two-day test will also be a crucial chance to trial new updates and further optimise the developments introduced ahead of Sunday's Spanish Grand Prix.
That will be most welcome for teams who failed to make as much progress they had anticipated, chief among them Toro Rosso and Sauber, who both spoke of the need to improve performance ahead of Monaco in two weeks' time.
Each of the 11 teams has also agreed to dedicate one day of in-season testing this year exclusively to tyre development. Toro Rosso and Sauber are the designated teams on Tuesday, with Wednesday the turn of McLaren and Force India. The tyres each team use will therefore not form part of the 135 sets they are allocated for 2014.