Anderson, loaned to the League Two club in January, helped them win promotion. The 19-year-old scored eight goals from 20 starts, including a strike in a promotion-winning 7-0 win over Scunthorpe United on the final day of the season.
Joey Barton’s team finished third, level on points and goal different with Northampton Town, and won promotion ahead of them on goals scored.
Howe had planned to send him to a club higher up the pyramid, but the loan, unquestionably, has worked for him and Rovers.
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“Very pleased for him,” said United’s head coach. “He was desperate to go and play, and have that experience on loan.
"I’ve said many times, I think, that we didn’t, initially, want to pitch him into League Two, because we felt that he was better than that level, but due to one reason or another that was the level he ended up at. He’s excelled.
"It’s difficult, as a young player, to go out and really make a difference, but he’s done that and made an incredible difference, I think, to Bristol Rovers. It was a dramatic final day, and credit to Joey, his team and Elliot.
"What an experience for him, and one he’ll always remember very fondly, hopefully at the end of a very successful career.”
Anderson is not eligible to play in Newcastle’s final two Premier League games, and Howe was asked if he would be loaned out again next season.
“We’ll certainly bring him back for pre-season,” said Howe. “I’ll have a close look at him. He’ll be involved in pre-season games. We’ll make a decision then on whether he needs another loan, or whether he’s going to stay with us.”
Anderson was promoted to the club’s first-team squad last season by then-head coach Steve Bruce after impressing in training.
The Scotland youth international made his Newcastle debut in an FA Cup tie against Arsenal last year.
Former United midfielder Barton wants to take Elliot back on loan at Rovers next season.