Rosler was announced as Owen Coyle's replacement on Saturday morning and had to jump on a train from Carlisle, where he was set to oversee former club Brentford, to watch Wigan go down at Millwall for their fourth consecutive defeat.
Whelan is fully confident that the German is the man to turn the club's fortunes.
"When he applied for the job, I had in mind his record so I did fancy what he's done and I did like what he's done," the Wigan Observer quotes Whelan as saying.
"When I met him, I was convinced, I would say, in five minutes that this lad was what I thought I was looking for. He had the right attitude, he said the right things and I liked his attitude totally."
Rosler's first game in charge will be a trip to Slovenia's NK Maribor in the Europa League on Thursday before returning to league action at home to Bolton Wanderers on Sunday.