Executives at the security firm were lambasted earlier this month by British MPs after the recordings inside Brook House Immigration Removal Centre were broadcast on BBC’s Panorama.
Ben Saunders has now stepped down from his role at the centre, near Gatwick Airport in West Sussex, England, and a temporary replacement will take up the post from Monday, G4S said.
Ten members of staff were suspended following the broadcast, of whom three have been dismissed.
G4S commissioned an independent inquiry and was assisting a police investigation, the British House of Commons Home Affairs Committee heard last week.
British Labour MP Yvette Cooper said it was a matter of "very grave concern" that the company appeared to have failed to get a grip on staff misbehaviour following earlier revelations of mistreatment at a young offenders’ unit.
Jerry Petherick, managing director for G4S custodial and detention services, said on Friday: "Ben Saunders has resigned from his role as director of Gatwick Immigration Removal Centres.
"Lee Hanford will be taking up the role of interim director with effect from Monday 25th September pending the eventual appointment of a replacement director."
Undercover BBC footage allegedly showed staff mocking detainees who were receiving medical treatment after self-harming or taking drugs.
In one incident, a detainee was self-harming by trying to self-strangulate and putting a mobile phone battery in his mouth.
A custody manager allegedly remarked: "Plug him in and he’ll be a Duracell bunny."
It was claimed that later during the same incident, when the detainee was being physically restrained, another member of staff was filmed choking the detainee.
Panorama’s undercover reporter said the staff member "basically stuck both of his fingers into his neck, and he was pushing so, so hard I could hear the detainee trying to gasp for breath".
G4S regional president for the UK and Ireland Peter Neden told the committee he had been left feeling "ashamed" of what he had seen and apologised.
Brook House is one of two immigration centres run by G4S in the UK and has capacity for 508 adult men.
Panorama uncovered alleged abuse and mistreatment of youngsters at a G4S youth detention centre in Kent last year.
Medway Secure Training Centre was later judged inadequate by Ofsted inspectors, who found that young inmates were able to watch sexually explicit content on television.
Another G4S facility, HMP Birmingham, was hit by riots in December 2016, some of the worst in a UK jail in years.