The former Chelsea man has made an instant impact since his January arrival.
"He has been absolutely fantastic - just what the supporters have been looking for," Rush told Liverpoolfc.com.
"He's a natural goalscorer. The goal he scored against Manchester City, there was no backlift, it was a fantastic strike.
"Before he came, the opposition focused mainly on Luis Suarez and Stevie [Gerrard] but with Sturridge, there's an added danger. He seems to gel well with Suarez and Stevie.
"He gets the tap ins as well. [In the past] we've had plenty of great shots where the ball has hit the post and come back or the keeper has saved and we've just been looking for someone to come along and tap the ball in. Sturridge does that.
"Also, his first touch is incredible in and around the box. He's very skilful and he's got a bit of pace. He can drift out to wide left, out to wide right and he can play through the middle."