The move will mean their funding will increase over the next four years but their entitlement to the group's profits will halve in the long term.
Under the existing arrangement, the foundations are legally entitled to 1 per cent of the group's annual profits. Under the new covenant, the foundations will receive a fixed grant for the next four years, to cover the period when the group is expected to be unprofitable. After 2013 the foundations will receive 0.5 per cent of the group's profits.
Linda Kelly, chief executive of the Lloyds TSB Foundation for England and Wales, said both the foundations and the group had agreed that the covenants needed to be renegotiated after the group lost huge sums in the credit crunch, which would have translated into a huge drop in funding for the foundations.
Kelly pointed out that the group was much bigger after the acquisition of HBOS last year, so halving the percentage of group profits would not translate into a halving of income. "The issue isn't the percentage: it is how much income we get," she said. "A lot of small and medium-sized charities rely on us and to have had no money for four years would have been terrible. We are trying to ensure we have as near guaranteed income as we can."
She said her foundation would receive £25.2m in 2010, compared with £21.9m in 2009. Without the renegotiation it would have been £144,000, she added.
Mary Craig, chief executive of the Lloyds TSB Foundation for Scotland, said: "If the foundations have settled using the group's current proposal to us, it is hard to see how this can be in the best interests of the charities they support in their respective countries."
Martin Sime, chief executive of the Scottish Council for Voluntary Organisations, which wrote to the foundations asking them not to accept the agreements, said the news was disappointing.