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The Ulster hooker, 33, succeeds Paul O'Connell, who led Ireland to back-to-back Six Nations titles before retiring from Test duty after the World Cup.
Schmidt's 35-man squad for the Six Nations games against Wales and France includes four uncapped players.
Munster captain CJ Stander, Connacht lock Ultan Dillane, Ulster centre Stuart McCloskey and Leinster flanker Josh van der Flier are all included.
Leinster front-row pair Cian Healy and Mike Ross, along with Ulster flanker Chris Henry, have been omitted as they continue their recovery from injury, but are expected to return following the opening two games.
The squad includes the bulk of the 31-man group selected for the World Cup, as well as the two late call-ups, Mike McCarthy and Rhys Ruddock.
Tommy Bowe, Peter O'Mahony, Iain Henderson and Dan Tuohy are ruled out through injury, while Darren Cave is not named despite being close to making a return to action after several weeks on the sidelines.
Robbie Henshaw makes the squad despite having been out for six weeks with a broken hand.
Ulster's superior form in Europe, in comparison to the other Irish provinces, is reflected in recalls for wing Andrew Trimble, centre Luke Marshall and hooker Rob Herring.
Herring and Munster prop James Cronin are handed call-ups after failing to make the cut for the World Cup, while Leinster prop Marty Moore and Munster flanker Tommy O'Donnell are back after being unavailable for the tournament through injury.
Among those to miss out on initial selection are forward trio Robbie Diack, Dave Foley and Jordi Murphy.
Best, the most experienced member of Schmidt's squad, has been handed the captain's armband ahead of Jamie Heaslip, Sean O'Brien and Johnny Sexton, who were all considered to be candidates for the job.
The Ulster hooker has 89 caps and has already captained Ireland four times.
Heaslip has led Ireland 12 times, including the World Cup quarter-final defeat by Argentina in October, while O'Brien captained the side in a game against Scotland last August.
The Ulster skipper was favourite for the position and his case may have been strengthened by reports of his half-time rallying call which contributed to the province's dramatic comeback victory over Oyonnax in their recent European Champions Cup pool game in France.
Ireland open their Six Nations campaign against Wales at Dublin's Aviva Stadium on 7 February, followed by an away game against France six days later.
Forwards: Rory Best (Ulster, captain), Richardt Strauss (Leinster), Rob Herring (Ulster), Sean Cronin (Leinster), Jack McGrath (Leinster), James Cronin (Munster), Ultan Dillane (Connacht), Nathan White (Connacht), Marty Moore (Leinster), Tadhg Furlong (Leinster), Devin Toner (Leinster), Mike McCarthy (Leinster), Donnacha Ryan (Munster), Rhys Ruddock (Leinster), CJ Stander (Munster), Sean O'Brien (Leinster), Tommy O'Donnell (Munster), Josh van der Flier (Leinster), Jamie Heaslip (Leinster).
Backs: Conor Murray (Munster), Eoin Reddan (Leinster), Kieron Marmion (Connacht), Jonny Sexton (Leinster), Paddy Jackson (Ulster), Ian Madigan (Leinster), Robbie Henshaw (Connacht), Jared Payne (Ulster), Stuart McCloskey (Ulster), Luke Marshall (Ulster), Luke Fitzgerald (Leinster), Keith Earls (Munster), Dave Kearney (Leinster), Andrew Trimble (Ulster), Rob Kearney (Leinster), Simon Zebo (Munster).
Rory Best has been chosen as the new Ireland captain by coach Joe Schmidt.