Botham, the former England allrounder who now acts as chairman of Durham, feels Rashid is "the best spinner in England" and added he did not have much sympathy for Yorkshire, who expressed public dissatisfaction at the selectors' decision.
Rashid's selection has drawn criticism from some quarters. Yorkshire's director of cricket, Martyn Moxon, had said he was "pretty disappointed" by the call-up despite Rashid telling the club he only wanted to play limited-overs cricket for them this season, while the club's former captain, Michael Vaughan, dubbed Rashid "unprofessional".
But Botham feels the selectors are "absolutely right" and believes both sides could field at least two spinners in the first Test at Edgbaston.
"He's the best spinner in England at the moment," Botham said of Rashid. "He's possibly the best one-day bowler in the world - he's certainly right up there - so why shouldn't he play? His Test record isn't bad.
"It won't make any difference to him that it's a red ball instead of a white one. He's not a swing bowler. He will get the ball to dip and spin because of the purchase he gets on it. The bigger seam on the Duke's ball might be better for him.
"There's a strong case for England to play two spinners at Edgbaston because of the way it turns. It wouldn't surprise me if India play three spinners.
"I hope he does really well. I like the kid. His bowling has come on leaps and bounds so I wish him all the very, very best."
With Rashid told by the England selectors he will have to play first-class cricket at county level in 2019 to be considered for Test selection, Botham hopes he can tempt him north to Durham.
"We will definitely talk to him," Botham said. "Of course we will.
"It is very competitive out there and everyone wants to get out of the second division. We won't do it this year but we'll do it next year with the way we are going and the way we are restructuring. We need to make it a side that people like Adil Rashid will look at and say 'it is only up the road and I can see where they are going and I would happily go there'.
"It is very hard to have much sympathy for Yorkshire. I have lost players - we have lost five key players at Durham - that have been poached around the north. I say poached and I stick by it.
"I have seen some pretty ridiculous stuff written over the last couple of days and I am very much on Adil's side."
Sir Ian Botham was speaking at the launch of his new wine range, Botham Wines. To pre-order from the range, visit bothamwines.com