Pujara is one of the key players in the Indian Test team, providing solidity to the batting line-up with his technique. His stint will be from 12 April to 22 May.
Ashwin, 33, who will play for Delhi Capitals in the upcoming Indian Premier League, will be Yorkshire's main overseas spinner following South African Keshav Maharaj's stint in 2019.
Highlights, England vs Pakistan, 2nd Test, Day 1 at Headingley, Full Cricket Score: Hosts trail by 68 runs at stumps
Catch all the LIVE scores and updates from the second Test between England vs Pakistan at Headingly
Australia's Matt Renshaw continues dream county run with second century for Somerset against Yorkshire
Australia opener Matt Renshaw's superb start in county cricket continued on Saturday when he scored a hundred before lunch for Somerset against Yorkshire – his second century in as many matches
Morkel Morkel, 33, took 309 wickets in 86 Tests at an average of 27.66 and was a member of the South Africa side that topped the International Cricket Council's Test rankings in 2012.
Kumar Sangakkara calls for minimum Test pay for all countries to stop young players ditching the longest format
Sangakkara praised the shorter format for spreading the game's popularity to new markets but warned that without change Test cricket could face a battle to remain relevant
Middlesex's Australian captain Adam Voges conceded his team had been outplayed but was not impressed by the state of the pitch.
Nitin Menon will be umpiring in the Leicestershire versus Sussex match from 9-12 June and Worcestershire's game against Kent from 19-22 June.