Alkass Digital
The 20-year-old, who is of Pakistani heritage, was initially left in Abu Dhabi when England travelled from their training camp to Hyderabad on Sunday.
On Tuesday, it emerged that he had returned to the UK, and the issuing of the visa was confirmed on Wednesday.
"We're glad the situation has now been resolved," said the England and Wales Cricket Board.
"Shoaib Bashir has now received his visa, and is due to travel to join up with the team in India this weekend."
A spokesperson for the Indian Foreign Office said: "The visa has been issued by London.
"There are rules and regulations governing the issuance of an Indian visa. The same were being applied in this case."
Somerset off-spinner Bashir will miss the first Test against India, which begins on Thursday.
Speaking earlier on Wednesday, England captain Ben Stokes said there was "never a chance" England would boycott the opening match of the five-Test series in support of Bashir.
He admitted he had floated the idea of a boycott among the team, but said it was "tongue in cheek".
"As a leader, as a captain, when one of your team-mates is affected by something like that you do get a bit emotional," Stokes said. "I'm devastated for him."
The uncapped Bashir, born in Surrey, was a surprise call-up to the England squad for this tour, having played only six first-class matches.
There are long-running political tensions between India and Pakistan, and he is not the first cricketer of Pakistani origin to struggle to gain access to India.
Australia opener Usman Khawaja, who was born in Pakistan, had his arrival for a Test tour last year delayed, while the entire Pakistan squad for last year's World Cup in India faced similar delays.
BBC Test Match Special commentator Aatif Nawaz, whose family are from Pakistan, also faced delays in receiving a visa for the World Cup and ultimately did not travel to the tournament.
Bashir's fellow England spinner, Rehan Ahmed, is also of Pakistani origin but has a visa from last year as he acted as reserve for the World Cup squad.
On Tuesday, a spokesperson for Prime Minister Rishi Sunak said the government expects British citizens to be treated fairly by India.
"I can't speak to the specifics of this case. But more broadly we have previously raised issues of this kind with the high commission. We have been clear that we expect India to treat British citizens fairly at all times in its visa processes," said the spokesperson.