The Govan club recruited the 23-year-old goalkeeper from Port Vale in a three-and-a-half year deal on Monday with Matt Gilks moving to Wigan
Alnwick is Rangers’ third signing of the January window after Jon Toral and Emerson Hyndman signed loan deals from Arsenal and Bournemouth respectively.
Warburton said: “He has got to challenge. If a keeper comes in with a number two mentality you are in a weaker position.
“Wes has been outstanding this season. Matt had a number one mentality and Jak has to be the same.”
Alnwick, who started his career at Newcastle, promised Foderingham a challenge, saying: “I have confidence and I will push him” and insisted he did not need to take any counsel when he heard Rangers were interested.
He said: “I didn’t need to. I have known about them for so long, as a young kid you knew about Rangers and I knew I wanted to come here from the minute I found out.
“You can’t turn down a club like this. It is an unbelievable club.
“As soon you hear the name Rangers - it was a no-brainer for me.
“It is a top club, you don’t need anyone to tell you how big it is, where they have been in the past and where they are working towards in the future.”