The Wales youth international was on trial at the Addicks last season and has signed a two-year deal with the London club.
“We got Ryan down here in two spells - one with the U23s and latterly with the U18s,” Avory said of Viggars.
“ His very last game on trial was at Wigan up there in the league, and we won 4-3 with 10 men that day. Ryan had to lead the frontline for 60 minutes in that 4-3 win and made a very good impression that day and that convinced me and Anthony [Hayes, U23 boss] that we should take the opportunity to offer him a contract.
“And then of course he played latterly in the U18s’ end of season games as well. He’s a very robust individual, a very mature lad as well. I like his personality, very strong.
“I think his hold up play is good, the way he links in with other players. He has scored goals regularly for Sheffield United - I’ve witnessed that - and I think he’s capable in that respect in the box in particular, so I'm looking forward to him coming in and developing under Anthony in the U23s.”
Viggars, who was called up to the Wales U18 squad during his time at United, said on social media: “New chapter.
“Delighted to sign a professional contract at Charlton Athletic. Looking forward to the start of the season.”
Charlton start their League One campaign at home to Sheffield Wednesday on August 7.