The Cambridge-born defender has arrived at Fratton Park for an undisclosed fee, and he has signed a two-year contract with the option of a further 12 months at the League One club.
The 21-year-old found his way into Mikel Arteta's first-team squad for the 2021-22 season but was unable to make an impression on the pitch for the Gunners.
Swanson - who had been in the Arsenal ranks since 2006 - made the bench in 15 consecutive Premier League gameweeks but failed to make a single appearance for the team in the top flight.
The right-back leaves Arsenal without earning his first-team debut for the North London club, but he registered two goals and two assists in 12 Premier League 2 games for the Under-23s last term.
Swanson had previously amassed seven goals and two assists in 34 Under-18 matches for Arsenal and made three appearances in the Keuken Kampioen Divisie for MVV Maastricht during a loan spell in 2020.
As well as Swanson, Arsenal have also allowed fellow prospects Jordi Osei-Tutu and Daniel Ballard to leave on permanent deals for VfL Bochum and Sunderland respectively this summer.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen