The Leicester City youngster joined the club this week.
The youngster completed a move to Rangers earlier this week after his contract with the Premier League champions came to an end.
He only managed nine appearances for Claudio Ranieri’s side but is highly rated, and Warburton moved quickly to secure his signature.
Joe Dodoo scores the fourth goal for Leicester
He is the ninth new signing to arrive at Ibrox this summer as Rangers have added to their squad as they aim to challenge Celtic for the title next season.
And Warburton says that Dodoo agreeing to move to Scotland sends out a powerful message.
“It sends out a really powerful statement that Joe is prepared to leave England' s champions to come here. He's young with great potential,” he told the Daily Mail.
Joe Dodoo of Leicester City celebrates with the matchball at the end of the game
It remains to be seen what sort of role that Dodoo will play in Rangers squad next season.
They are somewhat short of options up front at present, with Martyn Waghorn and veteran Kenny Miller their best options.
Waghorn’s plethora of goals last season makes him the first choice in the team but should Dodoo impress in training, it would not be surprising to see him starring in Warburton’s team before too long.
Rangers manager Mark Warburton celebrates at the end of the match