Under White House prodding, the Air Force has signed an agreement to use NASA's space shuttle for at least eight flights a year for 10 years starting in 1988.

In return, the Air Force will get a discount when the National Aeronautics and Space Administration works out a new pricing policy for the start of fiscal 1989. The Air Force will pay a fixed fee at the start of each fiscal year, then a per-flight charge less than commercial and other government customers pay.

Under the agreement, the space agency will drop its opposition to an Air Force plan to buy 10 single-use unmanned rockets to orbit two satellites a year for five years starting in 1988. NASA had opposed the Air Force plan in Congress and at the White House, calling it a potential threat to effective and economic use of the manned space shuttle.

"This new agreement," a source in the Reagan administration said, "states that NASA and the Department of Defense will work together to ensure that the shuttle will be fully operational and cost effective."

NASA says it hopes the space shuttle will begin to break even in 1987, when it anticipates making 24 shuttle flights, a schedule it hopes to maintain for at least 10 years. The agreement with the Air Force calls for that service to use one-third of all shuttle flights for the 10 years starting in 1988.

The agreement also gives the Air Force the green light to pick, perhaps this week, a "winner" in the competition to provide the single-use rocket it will use to orbit secret satellites too small to make economical use of the shuttle.