Bruseth is thought to have left Shell earlier this month, and the oil group has started an internal and external search to replace him.
He is expected to join global oil and gas company BG Group, taking over its top comms position from Matt Peacock. Peacock had been at BG Group since 2008, but left in May to become comms director at the Vodafone Group, replacing Bobby Leach.
A spokesman for Shell confirmed Bruseth's departure but was unable to provide details of Bruseth's next move.
A BG Group spokesman said the company would not comment on 'market rumour'. Neil Burrows, group comms manager, has been working as BG Group's interim group director of comms.
Bruseth joined Shell in 2004, having previously worked as a senior associate partner at City PR firm Brunswick Group.
Separately, Shell last year lost Andrew Eddy, its director of comms and corporate affairs for the UK. He now works as an independent consultant to the oil and gas industry.
BG Group was created in 1997 when British Gas divested Centrica. Today the group has operations in more than 25 countries on five continents.
Last year BG Group was linked with a £54bn takeover by Royal Dutch Shell, Exxon Mobil and Petrobas. Although no bid ultimately materialised, the group is still seen as a prime takeover candidate given its strong gas production businesses in Brazil and Australia.
The firm reported that first quarter profits were flat, a result of the continuing political turmoil in North Africa, which has restricted its oil and gas production in Egypt and Tunisia.