The left back has become the Pilgrims' latest arrival of the close season.
Brown, 23, was part of the Poppies side which pushed the Pilgrims until the final day of the National League North season for the final play-off spot.
And for his eyecatching performances that season, Brown was named the Town Player of the Season, as well as being voted the Fans' Player of the Season.
Brown - who came through the Sheffield United youth system - has previously played for Sheffield FC and Buxton before joining King's Lynn for an undisclosed fee.
He joined Kettering after his Linnets contract was terminated by mutual consent.
Brown announced he would be leaving Kettering on social media in May.
He wrote: "My time at @KTFCOfficial has come to an end.
"What a season it has been, relegation favourites to play off challengers.
"Thank you to all at the club and the fans for making me feel so welcome from day one, looking forward to what the next chapter holds."