The midfielder, who celebrated his 21st birthday last week, joined the Baggies on a season-loan loan deal from Chelsea in the summer.
With the Albion rooted in the relegation zone, Gallagher has been one of the few positives in what – so far – has otherwise been a miserable campaign.
The England under-21 international has put in a number of impressive performances in central midfield and has also chipped in with two goals.
And he says he has felt at home in the West Midlands from the moment he arrived.
“I have enjoyed being here from the very first day,” Gallagher said. “Meeting all the boys, they have been great – they are all nice guys and made it easy for me to settle in quick and to enjoy my football.
“Then when I started playing and I kept myself in the team – that helped my confidence.
“I feel like I have improved a lot.
“I have shown people I can play at this level and I am good enough.
“So it’s now time to push on even more.
“You can never stop or take your foot off the gas.
“It’s been great and I hope I can carry on and help the team this season.”
Gallagher first joined Chelsea at the age of eight with Frank Lampard his favourite player while growing up.
His ultimate aim remains representing his boyhood club in the Premier League.
But the midfielder knows playing every week has been crucial to his development – with Gallagher enjoying successful loan spells in the Championship last season with Charlton and Swansea.
“I played 47 games in the Championship last season including the play-offs,” he continued. “I was at Charlton in the first half of the season and then Swansea in the second half of the season.
“They were both great loan spells for me even though they were both short I learnt a lot.
“With both teams I became a better player and better person and I did well, so I was ready to make the step up.
“Chelsea thought so too – they wanted me to play in the Premier League.
“So when West Brom wanted to sign me and there was a chance, I wasn’t going to turn it down.”
Gallagher admits he dreamt of playing in the Premier League even before he joined Chelsea at the age of eight.
“I have three older brothers who got me into football along with my dad,” he added. “Ever since a young age, I have loved it and dreamed of playing in the Premier League.”