Discovery actor alleged the Oscar victor had pinned him to a bed in his apartment when Rapp was just 14.
The final season will consist of eight episodes, instead of the typical 13 episodes that seasons one through five consisted of.
Scotland Yard is investigating Spacey, who was artistic director at London's Old Vic theatre between 2004 and 2015, over two allegations of sexual assault.
The 46-year-old actor said he was "very surprised by it all" and felt "very gratified by the response" which he has received from so many people and the public in general.More news: Co-op to sell cut price food after 'best before' date
As previously reported, the Star Trek: Discovery actor claimed in an interview with BuzzFeed News published on October 29 that the House of Cards star, 58, made unwanted sexual advances toward him at a party in 1986.
Rapp explained he is relieved to see the critical step in the right direction toward the abolition of a system which "allowed this sort of thing to continue".
Following Rapp's allegation, Spacey said in a post on Twitter he does not remember the alleged incident, but that "if I did behave then as he describes, I owe him the sincerest apology for what would have been deeply inappropriate drunken behaviour". It was considered likely that Spacey would be written out of the show.
Now "House of Cards" will move ahead for the final season but there could still be more as a couple of spinoffs are currently in the works that may eventually get picked up at Netflix in the future.