Oswell arrived at the club back in 2020 - but his first season saw the National League North concluded early after just 17 games due to the Covid-19 pandemic.
The striker, who is a product of the Crewe academy, scored a handful of crucial goals as the Bucks survived relegation on the final day of the 21/22 season.
His final season was plagued by injuries - and he missed much of pre-season before suffering a dislocated shoulder midway through the campaign as the Bucks slipped to relegation to the Southern Premier League.
Earlier this month, the Bucks confirmed they were in discussions with a handful of players, including Oswell, about potentially remaining at the club, however the striker has confirmed his exit via a statement on social media.
He said: "I would like to thank Telford for the last three years at the club. It has been a rollercoaster journey and there have been memories I will never forgot, especially the final game of the 21/22 season.
"Not being able to contribute to the team for long periods of last season has been more than frustrating, a feeling I'm sure many of the fans can relate to.
"Thank you to all the fan who gave me great support during the three years.
"I wish the club the very best for next season and beyond."
The striker made his name in the Cymru Premier, scoring 56 goals in 104 games for Newtown, before signing for Stockport County.
A further season of goals saw the striker bag 28 times in 47 games for County, prompting a switch to League Two outfit Morecambe.
His spell with the club lasted just a season and he moved to Wrexham - before he was brought to the New Bucks Head by Gavin Cowan in 2020.