WASHINGTON—The Biden administration will send Saudi Arabia shipments of bombs worth more than $750 million in the coming months, removing a major irritant between Washington and Riyadh, according to officials from both nations.

The deliveries will include 3,000 Small Diameter Bombs and 7,500 Paveway IV bombs, which have been on hold since President Biden halted the shipments in 2021 over Saudi Arabia’s punishing war in Yemen.

The shipments underscore White House attempts to woo Riyadh, hoping closer ties with the oil-rich kingdom will pay dividends in the administration’s final months. The Biden administration has been drafting a defense treaty with Saudi Arabia, as well discussing plans to provide assistance so the kingdom can acquire civil nuclear power.

The White House needs Riyadh’s help in its push for a cease-fire in the Gaza war and is trying to broker an agreement for diplomatic recognition between Israel and Saudi Arabia, an influential voice in the Islamic world.

Saudi officials have pressed the U.S. to resume weapons sales since Biden halted the shipments in an effort to prevent civilian casualties and to pave the way for a 2022 cease-fire in Riyadh’s war against Houthi rebels in Yemen—a decision that strained already-tense relations with Washington.

“The Saudis will view this as addressing a strategic stain on relations with the U.S.,” said Dana Stroul , who until December was the most senior civilian official at the Pentagon with responsibility for the Middle East.

Biden entered office vowing to treat Saudi Arabia as a “pariah” during the election campaign because of the war and the 2018 assassination of journalist Jamal Khashoggi . But he has backed away from that stance since, including in a 2022 trip to Saudi Arabia, when he attended a high profile summit meeting with Crown Prince Mohammed bin Salman, the kingdom’s 38-year-old day-to-day ruler.

Jon Alterman, a senior vice president at the Washington-based Center for Strategic and International Studies said the main reason for lifting the weapons ban “is to reward Saudi Arabia for its support on regional security issues, including but not limited to their openness to long-term normalization with Israel.” But it is also “a signal to the Houthis that there is less daylight between the Saudis and the U.S.,” he added.

The weapons will augment the Saudi air force’s capability to carry out precision airstrikes from their U.S.-made jet fighters, more of which could be sold to the kingdom in coming years, U.S. officials said.

The $290 million shipment of small diameter bombs, also known as GBU-39s, provides Riyadh with a 250-pound munition that can be launched from a distance to carry out precise attacks, including in urban settings. The $468 million in Paveway IV bombs provides a munition that uses lasers or satellites to locate its target.

“This is the capability that a modern Air Force requires,” a State Department official said.

Administration officials briefed lawmakers and congressional staff on the decision last week, telling them that the deliveries wouldn’t jeopardize the cease-fire in Yemen.

Saudi Arabia has improved its targeting procedures to mitigate the risk to civilians should it be drawn into another conflict, U.S. officials said.

“The Saudis have met their end of the deal, and we are prepared to meet ours, returning these cases to regular order through appropriate congressional notification and consultation,” a senior Biden administration official said, referring to Riyadh’s truce with the Houthis and procedures to mitigate civilian casualties in future conflicts.

A Saudi official in Riyadh said the kingdom had been notified of the decision.

U.S. officials said the deliveries will likely start in several months. No additional weapons shipments have been announced by the U.S., beyond the two deliveries of bombs, administration officials and congressional aides said.

The U.S. imposed an initial ban on some arms shipments to Riyadh in 2016, following Saudi strikes on a funeral hall in San’a that killed at least 155 people and injured 500 more, the deadliest single bombing of the Yemen war. The Trump administration lifted some restrictions and approved a $110 billion arms sale.

The weapons ban Biden imposed in 2021 cut off “support for offensive operations in the war in Yemen, including relevant arms sales,” he said at the time. The U.S. continued sending Riyadh what it described as defensive weapons.

The U.S. sent half a million U.S. troops to the kingdom in 1990 to repel Iraqi dictator Saddam Hussein ’s invasion of Kuwait and defend Saudi oil fields. The relationship has also suffered serious strains, including over the Sept. 11, 2001, terrorist attacks in which 15 of the 19 hijackers were from Saudi Arabia and the 2018 murder by Saudi operatives of Khashoggi, a critic of the monarchy.

Write to Nancy A. Youssef at nancy.youssef@wsj.com and Michael R. Gordon at michael.gordon@wsj.com