Oswell, who endured an injury hit final season as the Bucks suffered relegation to the Southern Premier League, announced his exit from the club via Instagram on Wednesday.
Later on Wednesday it was confirmed the 30-year-old had returned to the Welsh club, where he had previously scored 54 goals in 106 games.
Oswell, who also netted twice for Newtown in the Europa League back in 2015, said there was only one club he was going to sign for upon exiting Telford.
He said: "I’m delighted to be back.
"Once I’d decided to leave Telford there was only one club that I wanted to play for. I can’t wait for the season to start.”
Oswell's form in Wales alerted Stockport County, with the striker going on to score 28 times in 47 games for the Edgeley Park club.
Spells at Morecambe and Wrexham followed before he arrived at Telford - but he endured a difficult three seasons plagued by the pandemic, relegation fights and it ultimately ended in relegation.
Now he will return to Latham Park and link up again with former Bucks forward Aaron Williams.
Newtown boss Chris Hughes added: "We’re absolutely delighted to welcome Jase back.
"All of the supporters will remember what Jason did in his three seasons with us and we’re excited to seeing him reunite with Aaron Williams to form what we hope will be a prolific partnership."