Published: 2018-08-07 04:55:46 BdST
He is the first India player since Sachin Tendulkar in June 2011 to lead the rankings and ends Smith's 32-month spell at the top, moving five points clear of the former Australia captain, who is serving a 12-month ban for ball-tampering.
Kohli scored 149 not out and 51 in India's 31-run loss to England in the first Test at Edgbaston but must remain in form during the rest of the four Tests in the series to stay top.
The 29-year-old, who also leads the one-day international standings, becomes India's highest-ranked Test batsman with 934 points.
Rahul Dravid, Gautam Gambhir, Sunil Gavaskar, Virender Sehwag and Dilip Vengsarkar are the other India batsmen to have achieved number-one rankings during their careers.
England seamer James Anderson retained his place at the top of the Test bowling rankings after four wickets in Birmingham ahead of the second Test at Lord's which starts on Thursday.