Jennings replaced injured opener Haseeb Hameed in the squad in the build-up to the fourth Test in Mumbai, which starts on Thursday at 04:00 GMT.
The 24-year-old is the son of former South Africa coach Ray Jennings, and captained South Africa Under-19s.
"The more time you spend in a country, the more you feel welcome," he said.
"Especially in the North East, the people are very welcoming - and that made me feel part of the furniture essentially.
"At the moment I'm feeling very comfortable and very English, despite my accent."
Jennings, whose mother was born in Sunderland, has served a four-year qualification period to be eligible for England.
The Durham batsman made 101 not out as he captained the England Lions against the United Arab Emirates last week.
He said the moment Lions head coach Andy Flower told him he had been called into the senior squad was "surreal".
"I texted my dad and it ended up with my dad being speechless and my mum in tears," he told BBC Sport.
Jennings said all-rounder Ben Stokes, his Durham team-mate, was helping him settle in to the national set-up.
"It makes it easier when you have Stokes taking the mickey out of you," he added.
England trail India 2-0 in the five-match series.
India's cricket board is considering whether to switch the final Test from Chennai following the death of a local politician.
The fifth Test is due to be held in the city from 16-20 December.
Keaton Jennings, the South Africa-born batsman who is set to make his England debut in India this week, has said he feels "very English".