Encouraging data from trials of three potential COVID-19 vaccines, including a closely-watched candidate from Oxford University, also supported sentiment and weighed broadly on the safe-haven greenback.
Against a basket of currencies the dollar traded at a more than four-month low of 95.687 while the pound extended overnight gains to a one month high of $1.2683.
The New Zealand dollar rose 0.2% and the Australian dollar added 0.1% to hold above 70 U.S. cents. The Japanese yen was steady at 107.23 per dollar.
"The agreement in Europe on the economic recovery fund underwrites growth there and improves the global economic outlook," said Commonwealth Bank of Australia FX analyst Joe Capurso.
"That is a positive for growth-linked currencies such as the Aussie and kiwi."
EU Council President Charles Michel said he was confident the compromises he offered the 27 leaders would clinch a deal on a fund that many say is critical to dispel doubts about the bloc's very future.
Michel proposed that within the 750 billion euro recovery fund, 390 billion should be non-repayable grants, down from 500 billion originally proposed, and the rest in repayable loans.
On the vaccine front, drugs developed by Britain's AstraZeneca with Oxford University and by CanSino Biologics with China's military research unit showed they were safe and produced an immune response in early trials.
Traders' focus on Tuesday in Asia is on Australia's central bank, which releases minutes from last month's meeting at 0130 GMT and a speech from Governor Philip Lowe at 0300 GMT.
The bank struck a more downbeat tone in its June statement than it had the previous month, so the minutes will be parsed for any shifts in thinking.
Lowe's speech, addressing the virus and labour markets, also comes as Australia fights a fresh outbreak of COVID-19 in Victoria state which authorities said could take weeks to subside even with a new lockdown in Melbourne.
"We are in a very different situation to where we were a month ago in terms of the virus - how rattled are they, if at all, on that" said Westpac FX analyst Sean Callow.
"Is Lowe worried enough that he is willing to talk about what might be the next step"
The Aussie was last a touch firmer at $0.7025. The kiwi held at $0.6581, close to the top of its range this month.
Meanwhile the pound hung on to broad and sizeable gains made overnight as many traders closed out long euro/pound positions in the wake of the EU Summit progress and ahead of fresh Brexit talks beginning on Tuesday.
Against the pound, the euro held close to a week low at 90.40 pence after dropping half a percent on Monday.
The two sides will resume talks on Tuesday after Britain's chief negotiator David Frost hosts his EU counterpart Michel Barnier for dinner later on Monday.
(Reporting by Tom Westbrook; Editing by Sam Holmes) ((email@example.com; +65 6318 4876;))