The 18-year-old, a product of the Gunners' youth system, will spend the rest of 2018/2019 in the Bundesliga in a bid to enjoy more first-team football.
"Reiss is a talented young player and we're pleased that he has signed a new contract with us," Arsenal boss Unai Emery said.
"This move to Hoffenheim will give him the chance to get regular high-level competition in the Bundesliga and is an important step in his development."
Hoffenheim will also compete in this season's UEFA Champions League, having finished third in the Bundesliga in 2017/2018.
It was drawn against Manchester City, Shakhtar Donetsk and Lyon in a tough-looking Group F.
Nelson made three appearances in the Premier League last season, as well as five in domestic cup competitions and eight in Arsenal's run to the UEFA Europa League semi-finals.