The 27-year old netted 35 goals for the club in his last spell and wants to replicate that goalscoring form for the Cherries in the Premier League.
But either way, the striker is delighted to return to the club and admitted he always wanted the club to do well despite being in a promotion battle for Norwich with the Cherries last season.
"I'm very pleased to be back here with the lads and back with the manager," Grabban said.
"I'm really happy to return and I want to pick up where I left off.
"It was largely successful at Norwich as we got promoted but this season I had limited opportunities for various reasons. I think I did OK when I came in but now I want to keep progressing with AFC Bournemouth.
"The lads in the dressing room were positive with me today when I returned and I kept in regular contact with some of the lads after I left. Now I'm back with them on a full-time basis and I can't wait to get going."
Grabban was involved in a promotion battle last season with the Cherries for Norwich and the striker revealed he always wanted the Cherries to do well despite being in direct competition with them.
"Last season was weird, being so close to Norwich in the table but I think each club knew what step the other was taking," he continued.
"I wanted AFC Bournemouth to do well at the same time as we were competing for promotion, but we both ended up in the same place anyway.
"But I'm glad to be back and it's changed a lot since I left, the facilities have improved and that will only benefit the club in the long run."