Just talk to Seneschal Varel about Velanna's joining and she will become a Grey Warden.
(Important) If the Blackmarsh is your last area to finish, do it AFTER you do Vellana's joining because the completion of the Blackmarsh will provoke the Final Quest, The Assault on Amaranthine. You will NOT be able to talk to Varel about having Velanna becoming a Grey Warden because he is busy with other concerns. This is true for Sigrun aswell.
Also, if the Knotwood Hills is your last area to finish, you will NOT be able to complete this quest for the reasons given above.
(This has been tested on the PC version, the PS3 version, and the Xbox 360 version.) It is recommended that if Knotwood Hills is your last area, that you leave before the final fight (there is an exit to Knotwood Hills just before you enter the Lower Levels) so you can return to Varel for the joining. Even though you don't ask her to join until after the battle, you can still make her undergo the joining.