Olsen and Willingham were introduced at a 3:30 p.m. ET news conference at Nationals Park.
Olsen figures to be part of a Nationals rotation that finished with a 4.97 ERA this past season. The southpaw was 8-11 with a 4.20 ERA in 33 starts in 2008, throwing a career-high 201 2/3 innings.
"I'm just happy it's over," Olsen said in a telephone interview with MLB.com. "I was wondering where I was going to be. It brings a whole different set of challenges I didn't have before. Me and Josh are both looking forward to it."
How Willingham fits in with the Nationals is not known. He is a corner outfielder, and Washington already has Austin Kearns, Elijah Dukes and Lastings Milledge playing those positions. Willingham also has experience behind the plate, but that position belongs to Jesus Flores.
Willingham appeared in 102 games this past season and hit .254 with 15 home runs and 51 RBIs.
Bonifacio was slated to be the Nationals' leadoff hitter and everyday second baseman, but Anderson Hernandez gave a better impression at the position during the final two months of the season, hitting .333 with 17 RBIs. The switch-hitting Bonifacio, who was acquired from the Diamondbacks last July for reliever Jon Rauch, hit .243 with 14 RBIs, particularly struggling from the right side of the plate, where he batted .186 with the Nats.
Dean, 22, pitched for Class A Vermont, where he was 4-1 with a 1.57 ERA in 10 starts.
Smolinski, 19, played for the Gulf Coast Nationals, Vermont and Class A Hagerstown and hit .271 with four home runs and 33 RBIs.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.