Barlaser became the club's fifth summer signing, joining on a season-long loan from Newcastle while Purrington returned to Charlton on a permanent deal.
The 22-year-old, who has signed a new Magpies contract, spent last season on loan with Accrington, playing 45 times in Stanley's League One campaign.
The Millers fought off interest from other sides for the former England youth international's signature, with boss Paul Warne playing a key role in recruiting him to the AESSEAL New York Stadium.
Warne visited the Premier League club and gave a presentation on why Barlaser should join the Millers and it paid off.
Meanwhile, Purrington spent the second half of last season on loan at the Addicks and helped them win promotion to the Championship, scoring a goal in their League One play-off final victory against Sunderland.
He returned to pre-season training with the Millers but always had his heart set on going back to the Valley.
Charlton have paid an undisclosed fee, understood to be six figures, for the left-back, but the Millers have made a significant loss on the £300,000 they paid for him in January 2017.
He signed a three-year deal and he has flew to Spain to join up with the club's training camp in Malaga.
Purrington said: “It’s a great feeling to be back with the boys. I see that same togetherness feel that we had last year. I’ve seen that straight away with a hard session today.
"It’s a pleasure to be back, I can’t wait to get started. There is no better feeling now than being back especially after the unbelievable year we had last year."
Despite Paul Warne being in charge when Purrington was signed, he was not the one that the boss had identified as the left-back was a choice of newly-appointed head of recruitment Jamie Johnson.
Warne always rated Joe Mattock higher than Purrington, who played less than 30 games for the Millers.
Of his time in South Yorkshire, he said on Twitter: “Just want to say thank you to everyone @OfficialRUFC .
“Will always remember that promotion year and wish the club every success this season!”