Mr Begg, 45, from Hall Green, in Birmingham, who was held in the US-run military prison in Cuba for nearly three years, is suspected of attending a terrorist training camp and facilitating terrorism overseas, West Midlands Police said.
A 36-year-old man from Shirley, in Solihull, and a 44-year-old woman and her 20-year-old son, both from Sparkhill, in Birmingham, have also been arrested on suspicion of facilitating terrorism overseas.
All four were being held at a police station in the West Midlands, police said, while their three home addresses are being searched by officers from the West Midlands Counter Terrorism Unit. Vehicles and electronic equipment are being removed for forensic analysis.
Non-governmental organisation Cage, which campaigns for the rights of people detained during counter-terrorism operations and for whom Mr Begg is an outreach director, said it was "outraged" by his arrest.
Asim Qureshi, research director of Cage, said: "Cage calls on all defenders of civil liberties and the rule of law to stand up and protest against the serious curtailment of yet another victim."