The Chancellor said there would be a “deal dividend” and an economic “bonus” if Ms May is able to reach a compromise with the EU.
It comes despite the government’s spending watchdog having this week warned that the UK’s finances are worse off because of the Brexit vote.
Mr Hammond said a deal would result in a more optimistic outlook because current forecasts from the Office for Budget Responsibility (OBR) factor in the possibility of a no-deal exit.
And fuelling hopes that an agreement is imminent, the Chancellor said there had been “a measurable change in pace” in Brexit negotiations and “a really important step change” based on “shared enterprise in trying to solve a problem rather than posturing towards each other”.
Speaking at a meeting of the International Monetary Fund (IMF) in Bali, he told the BBC: “If we are able to get to a good deal for Britain as we leave the European Union I believe there will be a dividend, a deal dividend for us.
“The OBR’s forecast, which is the basis of our current projections for the economy and our fiscal position, is based on pretty much a mid-way point between no deal at all and an EEA [European Economic Area] solution.
“The deal that we’re trying to negotiate with the EU now represents an improvement from the point of view of the British economy over that mid-point and therefore should deliver us an upside in the form of higher economic growth and better outcomes than were otherwise anticipated.”
Labour dismissed the claims as “good-old fashioned spin”.
Ministers have previously claimed that their £20bn-a-year cash boost for the NHS will be funded by a “Brexit divided”, although the existence of such a windfall has been challenged by leading economists, including the respected Institute for Fiscal Studies.
As well as improving economic forecasts, Mr Hammond said a Brexit deal would also enable him to release some of the funds the Treasury has set aside to deal with the impact of a possible no-deal outcome.
He said: “If we are successful in negotiating that package, there will be an upside dividend in terms of the economy and, consequently, the fiscal numbers, so that’s the first bonus.
“The second bonus is that I’ve been holding a slightly larger fiscal buffer than would otherwise be necessary because of the degree of uncertainty that exists at the moment.
“As that uncertainty is unwound and we’re in more favourable circumstances, logically, one would need less of a fiscal buffer and some of that could be released to support the spending envelope or to deliver tax cuts.
He was speaking after the OBR warned that a no-deal Brexit would result in a “severe short-term impact” on the UK economy, including a potentially sharp fall in house prices.
Overall, it is “noteworthy” that estimates suggest the UK economy is between 2 and 2.5 per cent weaker as a result of the decision to leave the EU, the watchdog said.
Responding to Mr Hammond’s claims, John McDonnell, the shadow chancellor, said: “This all smacks of good old-fashioned spin.
“It looks like Hammond is desperate to save his and the prime minister’s skins by dressing up a classic ‘put it off’ fudge as a deal, which will fail to provide the long-term security and certainty investors and businesses need.
“It appears that Hammond is planning a few tax conjuring tricks in the Budget to kid people that austerity is over when the reality is that the vast bulk of the cuts are still rolling out. We need a Chancellor not a conjuror.”
The Independent has launched its #FinalSay campaign to demand that voters are given a voice on the final Brexit deal.