The two sides confirmed an announcement from mediator Pakistan, with a signing ceremony set to take place in Switzerland on June 19, bringing an end to three months of conflict that has sent energy prices soaring and revived fears of another inflation spike.The Strait -- a vital maritime chokepoint through which roughly 20 percent of the world's crude oil supply transits -- was effectively closed by Tehran soon after US-Israel strikes on Iran launched the conflict."The Deal with the Islamic Republic of Iran is now complete," US President Donald Trump wrote on social media Sunday as he marked his 80th birthday."I hereby fully authorize the toll free opening of the Strait of Hormuz," he added. "Ships of the World, start your engines. Let the oil flow!"Iran's Deputy Foreign Minister Kazem Gharibabadi then said the deal put an "immediate end" to the war, with talks on a "final agreement" due within two months.The content of the agreement, which follows weeks of fraught negotiations and periodic threats from Trump of fresh hostilities, remained unclear.Crude prices tanked as much as five percent Monday, with West Texas Intermediate approaching $80 a barrel for the first time since the start of March. Brent was down nearly five percent at around $83.30.Both main contracts have come down since their initial surge past $110 soon after the conflict started.Missing detailsThe sharp drop in oil costs soothed growing concerns that soaring inflation could force central banks to begin hiking interest rates again.Data last week showing a jump in US May consumer prices -- coupled with strong jobs creation -- had ramped up bets on the Federal Reserve tightening before the end of the year."Oil down takes the inflation impulse down. Lower inflation risk takes some of the Fed-hike premium out of the curve. Lower yields give duration and growth equities room to breathe," said Stephen Innes at SPI Asset Management. "The dollar loses a bit of its wartime bid... in one headline chain, the market moves from bunker pricing to reopening pricing," he added.Traders will now have their eye on the next steps, he added, including the official signing in Switzerland, mine clearance and Israeli restraint.Michael Wan at MUFG sounded a note of caution."While it is certainly good news for the global economy and Asia that a deal has been announced, whether this sticks and remains viable depends among other things on the details of the negotiated terms," Wan wrote.Asian equities surged, led by Tokyo and Seoul, which both closed around five percent higher thanks to another flood into tech firms, fuelled by last week's record-breaking $75 billion IPO by Elon Musk's SpaceX.Shanghai, Sydney, Singapore and Taipei rose more than one percent while Hong Kong advanced 0.7 percent, and London, Paris and Frankfurt all had upbeat starts.Jakarta jumped more than four percent as easing concerns over energy costs provided fresh support to the beleaguered rupiah, which strengthened to 17,700 per dollar, its best level since the end of May. It had touched a record 18,209 earlier this month.Key figures around 0730 GMTWest Texas Intermediate: DOWN 5.3 percent at $80.37 a barrelBrent North Sea Crude: DOWN 4.7 percent at $83.26 a barrelTokyo - Nikkei 225: UP 5.0 percent at 69,317.50 (close)Hong Kong - Hang Seng Index: UP 0.7 percent at 24,892.18Shanghai - Composite: UP 1.6 percent at 4,096.47 (close)London - FTSE 100: UP 0.8 percent at 10,553.76Euro/dollar: UP at $1.1609 from $1.1577 on FridayPound/dollar: UP at $1.3437 from $1.3416Dollar/yen: DOWN at 160.06 yen from 160.23 yen Euro/pound: UP at 86.39 pence from 86.27 pence New York - Dow: UP 0.7 percent at 51,202.26 (close)