The Ministry of Defence will provide 40 defence medics and 160 general duty personnel for the next three weeks.
Hospitals in London have been hit hard by staff absences, with thousands off sick or isolating as the Omicron variant surged through the capital.
Earlier this week, the PM said he hoped England could “ride out” the latest wave without further restrictions.
Pressure on London hospitals has increased over the past month, with 4,000 patients currently in hospital with Covid compared with 1,100 in early December.
The Royal College of Nursing’s director for England, Patricia Marquis, said the deployment showed the government could not deny there was a “staffing crisis” in the NHS.
“The prime minister and others can no longer be dismissive of questions about the ability of NHS staff to deliver safe care,” she said.
Across the UK, about 1,800 armed forces personnel are supporting the NHS response to the pandemic.
As of Friday morning, 16 hospital trusts in England were experiencing critical incidents – about one in eight of the total.
A critical incident is declared when a trust is worried it might not be able to provide core priority services, such as emergency care. It means they can get extra help and draft staff in from other duties.
Approximately 4% of staff at acute NHS trusts in England were off because of Covid each day during the week ending 2 January, latest figures show.
That equates to 35,596 staff each day on average, up by 41% on the previous week.