The 26-year-old forward scored 21 points (11 goals, 10 assists) in 42 games with Detroit this season.
MacLellan said he envisioned Mantha playing on one of the Capitals' top three lines.
"I am comfortable on both wings," Mantha said.
Selected by Detroit in the first round (No. 20) of the 2013 NHL Draft, Mantha scored 194 points (95 goals, 99 assists) in 302 regular-season games.
He scored an NHL career-high 48 points (24 goals, 24 assists) in 80 games in 2017-18 and equaled that total in 67 games (NHL career-high 25 goals, 23 assists) in 2018-19.
Mantha scored 38 points (16 goals, 22 assists) in 43 games before last season was ended by the coronavirus pandemic, but his production dropped this season, the first of a four-year, $22.7 million contract (average annual value of $5.7 million) he signed Nov.
The 24-year-old has scored 25 points (11 goals, 14 assists) in 39 games this season after setting NHL career highs with 25 goals, 27 assists and 52 points in 69 games last season.
Selected by Washington in the first round (No. 13) of the 2014 NHL Draft, Vrana has scored 157 points (76 goals, 81 assists) in 284 regular-season games and eight points (three goals, five assists) in 38 playoff games.
Panik, who has scored nine points (three goals, six assists) in 36 games this season, will also get a chance to play more regularly with Detroit after the 30-year-old cleared waivers and was assigned to Washington's taxi squad April 8
The 32-year-old scored eight points (three goals, five assists) in 34 games with the Flyers and can be an unrestricted free agent after the season
"We like our center-ice position, but we wanted a guy that could play there if we needed it in a depth situation or we had an injury or if somebody was out for a few games, and I think he fits the bill there," MacLellan said