Niskanen received a seven-year contract worth a total of $40.25 million, while Orpik got a five-year deal worth $27.5 million.
New Capitals general manager Brian MacLellan stayed true to his promise to upgrade Washington's defense for new coach Barry Trotz.
Niskanen, a former first-round pick of the Dallas Stars, had a breakout season for the Penguins, registering 46 points in 81 games. The Capitals also hired former Penguins assistant coach Todd Reirden, who worked closely with Niskanen on defense in Pittsburgh.
The 27-year-old Minnesota native finished 11th in the Norris voting this season and has played in 491 career games since being selected No. 28 overall in the 2005 NHL draft. He has 35 goals and 132 assists in his career.
The 33-year-old Orpik has played his entire NHL career with the Pittsburgh Penguins, who drafted him in the first round in 2000.
The 6-foot-2, 219-pound Orpik has 13 goals, 119 assists and 734 penalty minutes in 703 career games.
The Capitals also signed goaltender Justin Peters to a $1.9 million, two-year contract.
The 27-year-old Peters went 7-9-4 with a 2.50 goals-against average and a .919 save percentage for the Carolina Hurricanes last season. He also played in six games for Charlotte of the AHL.
Peters made his NHL debut in February 2010, six years after being drafted in the second round by the Hurricanes.
ESPN The Magazine's Craig Custance and The Associated Press contributed to this report.