Both have run deficits for the past few years exceeding the 3 percent threshold permitted under the pact. Both faced possible EU sanctions which could have culminated in hefty fines.
With a number of other countries, Germany and France have long argued that the restrictions as applied so far damage economic growth.
The deal struck in Brussels introduces significant qualifications into how the pact is interpreted and gives governments wide latitude in justifying their deficits.
Luxembourg Prime Minister Jean-Claude Juncker chaired the meeting. He heads the EU's currents rotating presidency held by Luxembourg, and also acts as finance minister in his government.
Announcing the deal late on 20 March, Juncker was reluctant to divulge details, insisting only that the pact's criteria remain intact.
"We have not changed the fundamental rules of the Economic and Monetary Union, the criteria of 3 [percent of maximum permitted budget deficit] and 60 percent [public debt measured against the GDP] are not under threat and we have strengthened the preventive arm of the pact," Juncker said.
Officials say, however, that Germany won the right to deduct from its deficit the funds that go toward aiding former East Germany, estimated to come to some 4 per cent of the country's annual GDP.
France interprets another new clause in the pact as allowing it to deduct some defense and research costs from its deficit.
And new member states struggling with reforming their pension sectors were given a five-year reprieve, during which their deficits may breach the 3 percent threshold.
Juncker last night broadly justified the moves: "[We have agreed that] the pact will be applied in a more economic manner, that the interpretation of the grid used to read the pact will be more complete, that the pact will be applied over the entire duration of the economic cycle and that the [term] stability will not be lost in our vocabulary or practice."
Juncker was criticized earlier this month for trying to cut a deal behind closed doors with just the 12 members that have signed up to the euro present. The Stability and Growth Pact, however, can only be changed if all 25 member states agree.
On 20 March, Juncker indicated he believes he has everyone's support. He said he doesn't "think there will be a long summit discussion" on 22 March when EU leaders meet to examine the deal.
The attempts to relax the terms of the pact have long been seen as part of a campaign pursued by larger member states to limit the powers of the EU's executive, the European Commission, in their domestic policies.
Commissioner Joaquin Almunia, responsible for enforcing the Stability and Growth Pact, on 20 March made light of suggestions that the commission had lost the battle.
However, he was unable to explain clearly under what circumstances the commission could take action against member states after the Pact has been changed.
The new text allows for temporary budget overshoots that remain "close" to 3 percent of GDP if "relevant" factors exist.
Asked to spell out the precise meaning of the terms, Almunia simply repeated them.
"Close is close and temporary is temporary," Almunia said. "We are used to deal with these concepts since the beginning of this pact and since the beginning of the assessment of the Maastricht criteria. So, it's not new, we will consider all the relevant factors in assessing the situation of the public finances of a member state and we will consider [them] under the overarching principle that the excess over the reference value should be close and temporary."
The decision to change the terms of the Stability Pact follows admissions by EU leaders that its "Lisbon strategy" of economic renewal has failed. The main reason is a lack of economic growth, especially when compared to the United States.