Smith was released by Portsmouth at the end of the season, but Scott has moved quickly to secure the signature of the 34-year-old, who also spent a month on loan at Dartford late last year.
The 41-year-old told the club's official website: "Phil was somebody that we tried to sign on loan last year.
"There's an aura about him that will hopefully calm our defenders and they'll know that they've got somebody assured behind them.
"We kept 11 clean sheets last season and I'd like to get a few more of those."
Smith's transfer to Aldershot will not be officially completed until August 1.