Najar, who trained with Tottenham after the 2011 MLS season, joins a side that is eying another top-flight championship and just completed its run in the UEFA Champions League. Anderlecht currently employs American Sacha Kljestan.
"This is a good opportunity for Andy to continue training in the offseason and get another European training experience," D.C. United general manager Dave Kasper said in a team statement.
Najar, 19, was converted to right back from the midfield in his third season in MLS during a year in which he participated with Honduras in its run to the Olympic quarterfinals. He has three caps with the senior national team. Najar joins a host of MLS players who have gone overseas for training stints with European clubs, with Anderlecht joining the likes of Everton, Stoke City, Atletico Madrid, Real Sociedad, Derby County and Celtic as teams to open its doors to MLS talent.