No financial details where disclosed over the transfer of the left back, who joined Portuguese club Braga on a four-year deal from Stade Rennes in 2010.
Echiejile, 25, will be in competition for a first-team place with Layvin Kurzawa who has been in fine form this season.
Monaco are second in Ligue 1 with 42 points from 20 games, five adrift of champions Paris St Germain.
- Sports & Recreation
- Layvin Kurzawa
- Stade Rennes