Capps, 23, arrives at Scotstoun after a season with Stade Nicois in Federale 1, with the prop having benefitted from Scottish Rugby's performance partnership with the French outfit.
He has made 17 appearances in France this season, having previously played 10 games for Yorkshire Carnegie in the English Championship and British and Irish Cup.
Capps, who has represented England U18 but is Scottish qualified, becomes the second player to join the Warriors from Stade Nicois after Bruce Flockhart signed his first professional contract at the beginning of this season.
Nicol, 21, caught the eye with a series of impressive displays for Stirling County and signed his first-ever professional deal with the club ahead of this season, having made his debut for the Warriors against the Ospreys in November 2016.
He made his first start for Glasgow Warriors last October, playing 51 minutes of the bonus-point win over Zebre at Scotstoun.
The Scotland U20 international was part of the squad that secured an historic fifth-place finish at the 2017 World Rugby U20 Championship in Georgia. He packed down alongside current Warriors team-mates Matt Fagerson, Bruce Flockhart and Thomas Gordon, along with new signing George Thornton, who will join the club from Wasps next season.
Glasgow Warriors Forwards Coach, Jonathan Humphreys, said: "Adam has benefited from spending time in the environment here and we have seen him make big shifts, he has all the physical attributes to become a quality prop.
"Charlie has been playing in a physical division out in France and will add great strength in depth to the Glasgow front-row. Next season there will be five Scottish qualified props at Scotstoun aged 25 and under, which is excellent for both the club and Scottish rugby as a whole."