Just talk to Seneschal Varel about her Joining and she will become a Grey Warden. This can be done at any time after she joins your party--although for story purposes it does not make sense until the Silverite Mines are completed and she asks to become a Warden.
Also, if the Wending Woods was the last place you visited before the main battle that the Seneschal prompts, she cannot become a Grey Warden unless you travel to Vigil's Keep directly after Velanna joins the party AND another companion's joining quest is open (PC 1.04). MAJOR bug that was discovered.
Velanna will become a Grey Warden.