Joseph A. Califano, secretary of Health, Education and Welfare, gave final approval today to Virginia's college desegregation plan and said the federal government is prepared to defend it in court if necessary.

Califano's approval of the plan apparently ends 10 years of negotiations between HEW and the state and removes the threat that the federal agency might try to withdraw more than $75 million in annual college aid from Virginia.

Only a year ago, Virginia and HEW appeared headed for a courtroom showdown on the desegregation issue. Former governor Mills E. Godwin had rejected federal desegregation demands as enrollment "quotas" and Gov. John N. Dalton had appeared to support the Godwin position during his 1977 campaign for governor.

Shortly after taking office last January, however, Dalton ordered Attorney General J. Marshall Coleman and Secretary of Education J. Wade Gilley to try to negotiate a desegregation agreement. They succeeded last week, but only after their efforts almost foundered on a controversial elimination of duplicated programs at two Norfolk schools, predominantly black Norfolk State College and mostly white Old Dominion University.

The five-year desegregation plan provides for an increase in enrollment of 1,600 black students in predominantly white schools, now programs and facilities at those schools, scholarships to lure black and white students to colleges dominated by the other race and elimination of course duplications that HEW said perpetuate segregation.

Dalton and HEW have characterized the enrollment provisions of the plan as goals rather than quotas.

Virginia officials believe the state cannot be penalized for failing to reach the goals if it makes a "good faith" effort to do so.

HEW once approved a Virginia plan that was successfully challenged in federal court by black plaintiffs represented by the NAACP Legal Defense Fund. These plaintiffs still could chalenge the new plan, but Califano said in answer to questions today that HEW would defend it. Lawyers for the black plaintiffs could not be reached.

Virginia was one of 10 states whose plans were challenged by HEW and is one of only four that have obtained approval of new plans. Maryland, Louisiana and Mississippi are contesting federal demands in court. North Carolina, Georgia and Pennsylvania still are negotiating.

Califano said he hopes the Virginia plan can be used as a model to solve program duplication issues in North Carolina and Georgia.