The 29-year-old striker netted 13 times last season - and helped steer the Bucks to safety on the final day of the season after one of the most difficult campaigns in the club's recent history.
Oswell is one of the players who has agreed to stay on for another season - and is hopeful they can put their woes of last season behind them and climb towards the right end of the table.
He said: "It was tough last year, but I've enjoyed my time at Telford.
"I think the fans and the club respect the part I played last year in helping to steer the club towards safety - and I am hoping the club can now kick on and get to the other side of the table and avoid a relegation scrap."
Paul Carden has already bolstered his back line with the signing of York City defender Matt Brown and attacking right back Josh Dugmore.
Central midfielder Prince Ekpolo has also arrived with goalkeeper Luke Pilling also penning a new contract.
On top of that Zak Lilly, Jez Abbey and Callum Knowles have been offered new deals to stay at the club.
For Oswell, he insisted that despite having contact with other clubs during the close season he was always going to stay at the club if the deal was right.
He added: "There are other clubs I have spoken to, but for me I want to enjoy my football and work life balance, and on top of that, Telford is a big club.
"So as long as I was happy with the deal at Telford, I was always going to stay and I am.
"I feel like I am settled here and we have a good platform to kick on now.
"I want to be one of the leaders to help the gaffer push the team forward."
Bucks boss Paul Carden added: "I’m delighted that Ossy has decided to stay, the amount of managers who have asked me what’s happening with him during last season and the closed season has been endless.
"When I came to the club, I could see he was desperate to do well – in training he was working as hard as he could and his attitude was exemplary and as he got playing more his confidence increased and no one was happier than me to see him get his rewards in goals and important ones at that.
"We have spoke over the summer and he has his own targets for next season and I’ve set him some too.
"He has proven before what a good team player he is and backed it up with goals at higher levels. I’m pleased with how the squad is shaping and keeping Os is a big signing for us."