Armstrong, who previously thrived under Mowbray at Coventry and Blackburn, joined the Baggies on loan from Southampton.
Mowbray revealed that Albion moved quickly to secure the 27-year-old’s signature on deadline day when he became available.
"I've worked with Adam at a few clubs," said Mowbray. "I don't know his exact numbers, but over 20 goals for Coventry as a young boy and every season he was with me at Blackburn scoring over 20 goals and maybe over 30 one season.
"He's a talent. He's a great kid. He'll integrate into the dressing room straight away as his one session showed on Thursday.
"It's exciting. I think the players are excited Adam Armstrong is here to be honest. I'd have to say watching him in training he looked ready, sharp, quick, all the stuff we know he can bring.
"I'm looking forward to getting him going. Him realising which players can play the quality pass to slip him in to score. My overriding feeling was 'wow, we've got Adam Armstrong!' Hopefully we won't be thinking about where the goals are going to come from now."