The 34-year-old missed the drawn series in Bangladesh due to a stress fracture in his right shoulder.
He has been sidelined since August, but was cleared to head to India after a final test on Friday.
Anderson is set to arrive in Rajkot on Tuesday and miss the first Test, which begins a day later.
But his arrival is set to be a boost for England, who are in India for a five-Test series before limited-overs matches.
Meanwhile, fellow paceman Mark Wood has started his rehabilitation following his ankle operation.