The Costa Rica international has failed to get a work permit to play in England and has been sent out to the French club to develop and gain first-team experience
The 19-year-old, who joined the Gunners earlier in the summer, was unable to secure a work permit in the UK and so has been sent to the Ligue 1 club to gain experience playing football in Europe.
He arrived at the Emirates from Deportivo Saprissa for an undisclosed fee after impressing in the Under-20 World Cup and this summer's Copa America.
Lorient have also signed Giles Sunu from Arsenal earlier in a permanent deal.
The 20-year-old Frenchman, who can play in attack or midfield, signed a four-year deal with the Ligue 1 club.
A statement on the club's official website reads: "Everyone at Arsenal Football Club would like to wish both Campbell and Sunu well in northern France, and thank Gilles for his contribution to the club."
Arsenal have had a busy deadline day, with the announced signings of Brazilian Andre Santos from Fenerbahce and the imminent arrival of Per Mertesacker from Werder Bremen, while they have been linked with late swoops for Mikel Arteta and Yann M'Vila.