The Capitals signed the free-agent centre to a US$19.5-million, four-year contract on Monday.
Nylander is coming off a season in which he set career highs in goals (26), assists (57) and points (83) while playing for the New York Rangers.
The 15-year NHL veteran played for the Capitals between 2002 and 2004. He's posted 609 points (189-420) in 808 career games for Hartford, Calgary, Tampa Bay, Chicago, Boston, New York and Washington.
Nylander has had seven 50-point seasons during his NHL career.