The 24-year-old has been training with The Cherries since the beginning of the month after deciding not to accept a new contract with League Two club Yeovil Town.
Rodrigues's move completes his return to the South Coast club, having played for them in the 1998/99 season before joining Premiership side Southampton in a £170,000 move from Portuguese club Farense.
Cherries boss Sean O'Driscoll was keen to sign the striker again after losing the services of Warren Feeney to League One rivals Stockport County this summer.
Rodrigues was pleased to return to the club where he had his first spell in English football.
"I'm really looking forward to the start of the season because I think we can achieve something," the striker told the club's official website.
"I've had my problems with injuries, but now I can wipe the slate clean and hopefully get a good season under my belt."
The news comes as The Cherries have invited Jonathan Bewers and Michele Di Piedi to train with the club next week.
Bewers had been at Notts County last season while Di Piedi had a previous spell with League One rivals Sheffield Wednesday.
One player set to leave Bournemouth is Hungarian defender Krisztian Timar, who is facing three months on the sidelines with a knee injury.
Timar injured the knee in a pre-season friendly at Weymouth on Saturday, but O'Driscoll will keep an eye on the player and possibly bring him back at a later date.
Fellow Hungarian trialist David Disztl was unable to impress O'Driscoll during time at the club and has also returned home.
