The British discus record-holder joined the Super Bowl runners-up as an undrafted free agent, having impressed scouts at last month's super regional combine.
The 21-year-old told the San Francisco Chronicle: "[Defensive line coach Jim Tomsula's] background in NFL Europe was something that really appealed to me. Obviously, he's worked with guys that have hardly played the game before.
"He sees potential in me and he's made it clear that he wants to take me all the way. That's something I'm really happy about. I can't wait to work with him day in and day out.
"I'm not going to put any limits on myself. Nobody would have predicted when I was 18 that I would be the British record holder and an Olympic finalist."
Okoye, who played rugby union as a teenager, has never played a down of American football.