Thompson spokeswoman Linda Rozett said acting campaign manager Tom Collamore, former vice president of food and tobacco giant Altria, still will advise the campaign. Collamore has helped organize the campaign for Thompson, who has not officially jumped into the race.
Thompson has established a "testing the waters" committee that allows him to raise money for a presidential bid. He is expected to formally kick off his candidacy in September, after the Labor Day holiday.
"The Friends of Fred Thompson have made a number of changes as they prepare to enter the next phase, adding new experience and political strength to the organization," Rozett said.
Enright has served as Florida regional political director for the Republican National Committee and was executive director of the Republican Party of Iowa and the Republican Party of Florida.
Abraham is a former Michigan senator who lost a bid for re-election in 2000 to Democratic Sen. Debbie Stabenow.
Rozett said Enright and Abraham both would be in charge of Thompson's campaign. Enright is heading the political operation and Abraham doesn't yet have a title, Rozett said.
Scott Reed, a GOP strategist and campaign manager for Bob Dole's 1996 presidential campaign, said, "Collamore has put a good structure in place. Now the campaign can move to the next level with a formal announcement."
Thompson, the actor and former Tennessee senator, has not officially joined the nine-man Republican race but has raised several million dollars, hired staff and visited early primary states such as New Hampshire and South Carolina.