President Reagan, after smoothing out some objections in Congress, yesterday announced that he will nominate Harry N. Walters, an assistant secretary of the Army, to run the Veterans Administration.

If confirmed by the Senate, Walters, 46, would succeed Robert P. Nimmo, who resigned in October after criticism that he was insensitive to the special problems of Vietnam veterans and a charge that he had violated the law by using a federal chauffeur on personal business.

The Walters nomination had been delayed earlier this month when Sens. Alan K. Simpson (R-Wyo.), chairman of the Senate Veterans' Affairs Committee, and Strom Thurmond (R-S.C.), a committee member and one-time critic of Walters, complained to the White House that they hadn't been adequately consulted about the nomination.

Their complaints led the White House to interview Simpson's candidate for the post, Thomas E. Harvey, a heavily decorated Vietnam veteran and the staff director of the Senate Veterans' Affairs panel. But then the White House went ahead with Walters. Simpson was unavailable for comment yesterday, but an aide said the senator was now satisfied, would schedule an early confirmation hearing and would support the Walters nomination. Thurmond also expressed support for the nomination yesterday.

Since June, 1981, Walters has been assistant secretary of the Army for manpower and reserve affairs. A former All-American football player and New York businessman, Walters would be the first administrator of the VA not to have served in combat or wartime. When nominated to his current Pentagon post, he was criticized by Thurmond on grounds he had served only four years in the Army after graduating from West Point in 1969. Walters has said he left the service for a business career to support his family.

Before joining the Pentagon, Walters was president and chief executive of Potsdam Paper Corp., in Potsdam, N.Y., and had worked for other paper firms. After the troubled Nimmo period at the VA -- the third largest federal agency -- several veterans' groups said yesterday they welcomed the Walters nomination. "All we can do is hope for the best. Anything is going to be an improvement," said John Terzano, director of the Washington office of Vietnam Veterans of America.

Mylio Kraja, director of the Washington office of the American Legion, the nation's largest veterans' group, said that he hoped Walters would get "marching orders" to be "an advocate for veterans" in the post. He added that he saw "no problems" in the nomination after two meetings with Walters.

Veterans' groups have expressed concern that the new administrator be confirmed in sufficient time to participate in the drafting of the fiscal 1984 budget now under way. And the veterans' groups believe that Walters will face one of his earliest challenges if veterans' programs are targeted for deep budget cuts.

Walters appeared to acknowledge this recently in an interview with Alan S. Emory of the Watertown (N.Y.) Daily Times. "It's going to be me against [Office of Management and Budget director] David Stockman," Walters was quoted as saying.