Hinske, an infielder-outfielder, and the Diamondbacks agreed to their deal Tuesday at baseball's winter meetings in Nashville, Tenn. Nieves and the team came to terms on Wednesday.
A veteran of 11 major league seasons, Hinske spent the last three years with the Atlanta Braves. He hit .197 with two homers and 13 RBIs in 132 at-bats this year, seeing time at first base, left field and right field. He made three straight World Series appearances from 2007-09 with Boston, Tampa Bay and the New York Yankees.
The 35-year-old Hinske will fill a bench role for the Diamondbacks. He has a .218 average (57 for 262) as a pinch hitter with eight home runs and 36 RBIs.
Nieves, also 35 wasn't tendered a contract by Arizona last week. He batted .306 with a home run and three RBIs in 16 games for the D-backs in 2012.
Arizona claimed Nieves off waivers from Colorado on Aug. 6. Nieves was designated for assignment by the Rockies after hitting .298 with one homer in 16 games with the Rockies and .306 with three homers in 111 at-bats for Triple-A Colorado Springs.
Nieves has batted .229 (191 for 834) with seven home runs and 81 RBIs in 314 major league games over nine seasons. He has also played for San Diego, the New York Yankees, Washington and Milwaukee.