WS will take over the account next month following what is believed to have been a four-way pitch which also included Financial Dynamics and Tulchan Communications.
College Hill said its retained relationship with Cobham ended six months ago and that, since then, the FTSE 250 company had been working with the firm on a project basis. Cobham CEO Allan Cook was unavailable for comment.
WS Square Mile director John Coles will lead the account.
Cobham makes and sells fuel and fluid lines for the aerospace industry through its Aerospace Systems Group.
Last week, Cobham reported a 131 per cent rise in pre-tax profit for 2004. It made nearly £126m in 2004, up from £54.5m in 2003.
The firm has a 20 per cent stake in the AirTanker consortium, to which the Ministry of Defence awarded preferred bidder status for its Future Strategic Tanker Aircraft PFI programme in February.
If AirTanker is successful it will have a 27-year contract with the Royal Air Force.
Cobham is providing the air refuelling equipment for the A330-200 Multi-Role Tanker Transport chosen for the programme.
Last December, the company also benefited from the agreement of Eurofighter partner nations UK, Germany, Italy and Spain to press ahead with the second production tranche of 236 combat aircraft. Cobham makes fuel tubes and couplings for the Eurofighter via its Stanley Aviation subsidiary.