The 25-year-old striker has joins the League One club for undisclosed fee, signing a three-year deal at Fratton Park.
Hawkins has been linked with a move to the south coast all summer and finally a deal has been agreed.
The former Hemel player was fantastic last season as the Daggers reached the play-offs. Now, he is a Portsmouth player.
Pompey boss Kenny Jackett said: “We’re really pleased to get Oliver over the line and I’m looking forward to working with him.
“He’s someone I’ve watched for a long time and is capable of stepping out of Non-League and doing well for us, complementing the players we’ve already got.
“He will obviously add some physicality to our squad. He holds the ball up and is a big threat in the box – in fact he’s useful in both boxes.”