The Senate last night approved and returned to the House a "fast-track" bill ordering reorganization of the Farm Credit System and opening the way for federal financial aid if needed.

The House is expected to complete work on the rescue package today and send it to the White House for President Reagan's signature.

"We've taken the first step to assist rural America and farmers, as far as the Farm Credit System is concerned," Majority Leader Robert J. Dole (R-Kan.) said.

The legislation, calling for major changes in the Farm Credit System and giving the federal Farm Credit Administration more regulatory muscle, was rushed through both chambers as part of an effort to bolster investor confidence in the system.

Approval of changes without debate last night was part of a behind-the-scenes move by farm-state legislators to settle differences without a time-consuming conference and allow final passage before Christmas adjournment.

Recent record losses and the potential for more in the Farm Credit System, the nation's largest agricultural lender, prompted Congress and the administration to push for a reorganization that requires use of the system's assets before federal aid can be provided.

The legislation creates a capital corporation within the Farm Credit System which will oversee the transfer of funds from healthy banks in the system to needier banks.

The corporation also would take over unpaid debts by Farm Credit System borrowers and administer any federal aid.