White had been waived Sunday as part of some roster juggling tied to the overall 63-player snapshot (53 on roster, 10 on practice squad). His locker remained intact over the last few days, which was an indication that his return was likely.
Some have asked: Why would the Patriots waive White if they planned to re-sign him the whole time?
By doing so, and assuming the risk that the four-year veteran would clear waivers and later return, the Patriots opened up spots on their protected 53-man roster to bring in other players they were interested in working with this season. The team wouldn't have had the same leverage to bring those players aboard and take a closer look if they didn't claim them on waivers (e.g. Kelcy Quarles, Bruce Gaston).
There is also an element of timing to consider.
By staggering some of their roster decisions, practice squad signings and waiver claims, the Patriots appear to believe it gives them the best chance to form the most balanced and talented 63-player snapshot, eliminating competition from other teams that perhaps are already locked into their own rosters and practice squads.
In addition to bringing back White, the Patriots also confirmed the re-signing of long snapper Danny Aiken. Also, quarterback McLeod Bethel-Thompson has been re-signed to the practice squad to fill the open spot created by long snapper Charley Hughlett's release.