David Cameron also nominated Tory and Labour members, including former attorney general Dominic Grieve.
Mr Robertson was among a number of MPs who had called on the committee to investigate an RAF drone strike in which two British citizens were killed.
He is expected to use his position on the committee to re-affirm those calls for an investigation.
It was confirmed on Monday by the UK government that Cardiff-born Reyaad Khan, 21, and Ruhul Amin, from Aberdeen, died in Syria, alongside another fighter, in the first targeted UK drone attack on a British citizen.
The men had gone to the conflict zone to fight for the so-called Islamic State group.
Defence Secretary Michael Fallon said the drone strike was a "perfectly legal act of self defence".
He added that the UK would not hesitate to launch more secret drone strikes in Syria to thwart terror plots.
The new appointments to the intelligence and security committee, which can summon intelligence chiefs to give evidence, include;
The prime minister has appointed SNP MP Angus Robertson to Westminster's intelligence and security committee.