At WS, he headed the agency's crisis and issues management division.
At Lloyd's, which comprises 86 independent insurers trading under the Lloyd's brand, Peel takes on responsibility for all marcoms, community affairs and business intelligence for the group's global operations.
He replaces Caroline Wagstaff, who resigned after four years to take a career break, according to a Lloyd's spokeswoman.
Peel is set to take on the role of head of marketing and communications next month, reporting directly to Lloyd's CEO Nicholas Prettejohn.
He will oversee a team of 16 with a remit to oversee all in-house and external comms, including strategic PR advice to the board and lobbying work.
Peel said: 'Lloyd's has begun a reform programme that should ensure it remains a world leader in the insurance industry.
'Marketing and communications will be one of the keys to successful modernisation of Lloyd's,' he added.
Lloyd's, which was founded 314 years ago, began a process of modernisation in January this year with a view to updating its insurance market.
Peel formerly worked under Labour Party spin doctor Alastair Campbell during his time as a civil service PRO.
He joined Downing Street in 1998 from the Department of Education and Employment, where he was spokesman for the then Trade and Industry Secretary Stephen Byers.