Quatro said his appointment would add to the team’s capacity to "deliver high-level strategic advice".
The agency specialises in boutique political communications, with a range of client briefs that include international campaigns supporting nation-building and civil society engagement in war-torn countries to sustainable development projects and human rights campaigns.
Grant has previously worked for the Foreign and Commonwealth Office as high commissioner in Pakistan and served the UK’s ambassador to the UN for six years. He was national security adviser to two UK prime ministers – David Cameron, then Theresa May until 2017.
"We are thrilled to have Sir Mark join our team," Quatro managing director Gary Pleasants said. "His unparalleled experience and knowledge will help us provide in-depth strategic insight for our clients wishing to engage with the UK government on foreign policy and security matters, and in the international political arena.
"Sir Mark joining our team signals our ambition to significantly grow this sector of our business."
Grant added: "I am delighted to be working with Quatro and looking forward to engaging with some exciting and complex briefs. Quatro is a dynamic, forward-thinking agency and I hope to help them grow in this arena."