HITC Sport understands that the teenage goalkeeper is to link up with the League One new boys on a short-term agreement.
The 19-year-old is in need of first-team experience as he remains some way down the pecking order at the Amex Stadium.
He made his senior debut for the Seagulls in a League Cup clash with Tottenham Hotspur last season, while going on to make three appearances in the Championship.
Walton is, however, seen as one for the future and needs minutes under his belt if he is to fulfil his potential.
Bury are prepared to offer him a shot at senior football, with the club preparing for life back in League One.
Brighton will be looking for the England U20 international to get expose to competitive football with the Shakers, seeing him returned to them ready to push for a starting berth.
HITC Sport reported last week that a number of Football League clubs were battling it out to secure his services on a short-term deal, but it is Bury who have emerged victorious.