The new Baggies duo have earned rave review from former midfielder Dave Edwards, the ex-Wolves and Wales international, who played with Wallace and Swift at Molineux and Reading respectively.
Edwards lauded his former Royals team-mate Swift, last weekend's debut Championship goalscorer, as an attacking midfielder with 'Premier League top-half quality'.
The 36-year-old pundit told the Express & Star: "Swifty's a wonderful player and an unbelievable signing for West Brom. He has everything to be a top Premier League player. He can play in the top half of the Premier League.
"I'm really surprised a Premier League club didn't come in to take him. He's got everything you need to be a top midfielder.
"For large periods of his Reading career he delivered as well, so it's not as though he's got these unbelievable traits but he doesn't deliver on a matchday – he delivers consistently.
"It's a massive move for Steve Bruce to get his quality in. If they're looking to be at the top end of the table, to get someone like John Swift, who can create and score, it's the difference between drawing and winning a game, or losing and coming back to draw.
"It's the hardest thing in football to score and create goals and that's what he's brilliant at.
"I knew he was a good player when I signed for Reading but not for one second did I realise how good he was.
"You see in training his awareness, touch, his work ethic, the amount of work into how he strikes a ball. He's got such a different style to strike a ball from distance.
"It's something he's been coached on, he had his own set-piece coach at Reading, they would do sessions in the afternoon, he knew him from Brentford previously. You see the movement he gets on the ball.
"But he's much more than that, a complete attacking midfielder."
Swift spent 18 months as a team-mate of Edwards' in Berkshire, where the Portsmouth-born creator netted 33 goals in 202 appearances in total.
Edwards explained how the new recruit's physicality could also be a huge plus for Albion. He added: "He's got a physicality about him. I wouldn't say he's a tough-tackler by any means, he's a flair player.
"But his physical attributes in terms of his size, he's six foot, broad, strong, hard to get off the ball and he uses his body well.
"People might not see but when you train with him closely you see his running power with the ball. When he starts striding he's quick and hard to catch.
"It's another attribute in a Steve Bruce side which will at times play counter-attacking football, to have someone like John Swift carrying the ball and pick a pass will be a massive plus."
Edwards revealed Swift's 'quiet, unassuming and polite' character, before adding his former Wolves colleague Wallace, Bruce's acquisition from Millwall, can be the positive 'life and soul' of the Baggies dressing room.
He also described winger Wallace's drive on the pitch, as well as his personality, as infectious.
"Jed's such a likeable lad," he added. "He's the life and soul, always cracking jokes, winding people up. I think it's very important to have people like that, being a good, honest lad.
"He appreciates coming up through the leagues. He was in League Two with Portsmouth, got his move to Wolves and he was very unfortunate with his timing in that he didn't play as much as he should've.
"You could see he had bags of ability and potential, but it was a struggling Wolves team and he never got the minutes he deserved.
"He took a step back to go to Millwall, I'd say, and he absolutely smashed it. He brings you that contagious enthusiasm and energy on the pitch, he works so hard. It will drive players around him to that intensity.
"On the ball he's got quality. His biggest attribute is his pace, running at players, what he did on Saturday, running down the side, getting crosses in.
"He did so well at Millwall and probably could've moved two or three times in recent years but he remained loyal. He's not someone who is money-oriented, he wants to play where he's happy.
"He saw the West Brom project and maybe as an ex-Wolves boy it wasn't the easiest decision but I know he'll do well. He's very reliable."
On the duo combining at Middlesbrough, Edwards noted: "That won't be the last time they link, it can happen the other way with Swifty's vision, looking for those runs from Jed."