Coats defeated Democrat Brad Ellsworth for the seat being given up by Sen. Evan Bayh, a Democrat, The Indianapolis Star reported.
Election results posted by the state secretary of state's office showed Coats with 174,110 votes to 114,983 for Ellsworth.
Coats, a lawyer, most recently has been a lobbyist and U.S. ambassador to Germany since leaving the Senate in 1999. He had initially been appointed to the seat after Dan Quayle was elected vice president, then won a special election in 1990 and a full term in 1992. He didn't seek re-election in 1998.
Coats also served in the U.S. House from 1981-1989.
Growing GOP strength showed up in results of three House races thought to be toss-ups, CBS News reported.
In the 8th District, GOP candidate Larry Bucshon, a cardiologist, soundly defeated former prosecutor Trent Van Haaften, 108,901 votes to 71,544.
In the 2nd District, a Tea Party candidate came up just a percentage point shy of knocking off Democratic Rep. Joe Donnelly, who squeaked out a win with 91,328 votes to Republican state legislator Jackie Walorski's 88,786.
And in the 9th District, incumbent Democratic Rep. Baron P. Hill lost his seat to Republican former prosecutor Todd Young.