Stegmann had already agreed a two-year contact with the capital outfit, which was due to come into place from next season. However, the move has now been brought forward.
Quins boss Conor O'Shea said: "Given that Seb had already signed a two-year deal with London Welsh for next season, once Lyn Jones approached us looking for his early release, we felt it was in the player's best interests to allow him to do so.
"The selfish and easy thing for us to do would be to keep Seb and I know how much he was looking forward to contributing to both the LV= Cup playoffs and our run in for the remainder of the season."
Stegmann made his first-team debut for Harlequins in 2007.