However, John Battle, the Industry Minister, also announced that there would be a new limit of 15 per cent on individual foreign shareholdings in each of the companies.
The new limits will be enforced through the indefinite "golden share" that the Government holds in BAe and Rolls.
The increase in the ceilings was long-awaited and followed an intensive lobbying campaign by BAe and Rolls who argued that the restriction limited the marketability of their shares and depressed their share prices.
The request for a limit on individual shareholdings was contained in the joint application put to the Department of Trade and Industry by the two companies in July although it is understood that BAe would have preferred there to be no limits at all, either on overall or individual foreign shareholdings.
Shareholders will be asked to vote on the increase in the shareholder ceilings at the annual meetings of BAe and Rolls, due to held respectively on 29 April and 28 May.
Mr Battle said the relaxation in the ceilings was "designed to promote the competitiveness of these companies by increasing their freedom to operate commercially in the world markets".
Rolls chairman, Sir Ralph Robins, said the changes were consistent with the increasingly international nature of its business. Three quarters of its sales are exports or are generated outside the UK.
In recent weeks both companies have been pushing up against their 29.5 per cent ceilings in anticipation that the limits would be lifted.
The current level of foreign ownership in BAe is 29.14 per cent while Rolls is 27 per cent foreign owned. At privatisation in 1985 for BAe and 1987 for Rolls the limit on foreign ownership was set at 15 per cent. It was raised to the current level in 1989 after a number of forced sales after foreign shareholders had breached the limit.
A DTI spokeswoman said that to have raised the overall limit to 49.5 per cent but not to have imposed a lower ceiling on individual shareholdings would have defeated the object since a single foreign shareholder would have been able to gain an effective controlling shareholding without needing to bid for either company.
Rolls shares closed 14p higher at 268.5p on the news while BAe shares ended the day 20p up at 1935p. BAe said the increase in the limit would give it all the flexibility it needed.Reuse content