Analysts said that, while uncertainty about Greece's future remained, the deal turned investors' focus to a potential Fed rate hike in September after comments from central bank Chair Janet Yellen and Boston Fed President Eric Rosengren on Friday suggested that could be likely.
Yellen will give closely watched semiannual testimony to U.S. Congress later in the week.
"The Fed seems to be setting itself up to hike in September," said Steven Englander, global head of G10 FX strategy at CitiFX in New York. He said the Greek deal removed an obstacle to a Fed rate hike.
Read MoreGreece talks rumble on: Athens still has more to do
"If you take Greece off as an immediate issue," he said, "all of a sudden you say: 'What are the impediments to the Fed hiking?"'
The euro slumped nearly 1.46 percent against the dollar and hit a session low of $1.0996. It last traded down 1.45 percent at $1.10.
The dollar hit a more than one-week high against the yen of 123.535 yen, before trading up 0.57 percent at 123.42.
Analysts said a drop in oil prices also weighed on the euro as Iran and six world powers appeared to be closing in on a nuclear deal that would end sanctions on the Islamic Republic and let more Iranian oil into world markets.
"Oil going lower increases the probability of lower inflation globally," said Richard Scalone, co-head of foreign exchange at TJM Brokerage in Chicago. "That impacts Europe disproportionately, or more than the U.S."
The European Central Bank launched its 1 trillion euro bond-buying program in part to ward off deflation.
The dollar was last up 1.09 percent at 0.9491 Swiss franc. The dollar index, which measures the greenback against a basket of six major currencies, was up 0.82 percent at 96.82.