Hooker Best passed a fitness test on a calf strain and was named in the side by coach Joe Schmidt on Thursday for a remarkable 32nd consecutive Six Nations start.
Munster's experienced O'Donnell comes in for Josh van der Flier at openside in a bid to counter a Scotland back row that has been highly impressive in the tournament.
Keith Earls also wins his 50th cap on the left wing.
O'Donnell missed the 2015 World Cup with a hip injury and started the first match of the Six Nations against Wales last month.
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"Josh has shipped a couple of knocks in the last two games and he got a bump in training on Monday," said Schmidt.
"I think it's been pretty attritional for him going back-to-back in his first two test matches.
"He would be fit to play but at the same time is carrying a few knocks. Conversely Tommy has trained incredibly well," added Schmidt.
"He hasn't had the luckiest of preparations with us in previous times and we're looking forward to contributing a really athletic, combative performance this weekend."
Ireland, who came into the championship seeking a third successive title, have been hard-hit by injuries and have had a largely disappointing campaign.
A home draw with Wales was followed by away defeats to France and England before they finally chalked up a win by hammering Italy 58-15 last Saturday.
Scotland arrive on the back of a morale-boosting victory over France but Ireland have a terrific home record against their Celtic rivals, losing only once since 1998, at Croke Park in 2010
Team:
15. Simon Zebo (Cork Constitution/Munster)14. Andrew Trimble (Ballymena/Ulster)13. Jared Payne (Ulster)12. Robbie Henshaw (Buccaneers/Connacht) 11. Keith Earls (Young Munster/Munster) 10. Jonathan Sexton (St Mary's College/Leinster) 9. Conor Murray (Garryowen/Munster)1. Jack McGrath (St Mary's College/Leinster) 2. Rory Best (Banbridge/Ulster) (captain) 3. Mike Ross (Clontarf/Leinster) 4. Donnacha Ryan (Shannon/Munster) 5. Devin Toner (Lansdowne/Leinster)6. CJ Stander (Munster)7. Tommy O'Donnell (UL Bohemians/Munster)8. Jamie Heaslip (Dublin University/Leinster)
Replacements: 16. Richardt Strauss (Old Wesley/Leinster) 17. Cian Healy (Clontarf/Leinster) 18. Nathan White (Connacht) 19. Ultan Dillane (Corinthians/Connacht) 20. Rhys Ruddock (St Mary's College/Leinster) 21. Eoin Reddan (Old Crescent/Leinster)22. Ian Madigan (Blackrock College/Leinster)23. Fergus McFadden (Old Belvedere/Leinster)
(Reporting by Mitch Phillips; Editing by Tony Jimenez)
