The awards, which honour performances during a calendar year, saw Kohli walk into both sides which were selected by the ICC Voting Academy comprising former players, members of the media and broadcasters.
Kohli topped the run charts in 13 tests, scoring 1322 runs at 55.
Kohli was named to captain both sides, with team mate and fast bowler Jasprit Bumrah the only other player to make the test and ODI selections.
Reacting to the news, an elated Kohli said: "It has been an unbelievable year".
According to an ICC statement, pacer Jasprit Bumrah is the other Indian to make it to both the sides while stumper Rishabh Pant is the third Indian to find a place in the Test Team of the Year.
Three Kiwis have been named to the International Cricket Council's test XI of the year after the Black Caps' impressive run of four successive series wins. "Having recognition at the global level from the ICC is something you feel proud of as a cricketer because you understand that there are many players playing the game", Kohli said.
The 30-year-old Kohli, who first came into limelight when he led India to victory at the ICC Under-19 World Cup in Malaysia in 2008, finished the year as the top-ranked batsman in Tests and ODIs.
Rams' McVay knows PI call missed, but also saw Goff facemask
The Rams would then deliver the knockout blow with a massive 57-yard field goal to seal the game with a final score of 26-23. In both cases, it was the visiting teams coming out of the games with punched tickets to the Super Bowl .
10 crew members dead after 2 cargo ships catch fire near Crimea
The fire broke out when one vessel was transferring fuel to the other, driving both crews to jump overboard, said Mr Kravchenko. Russian Federation has moved to seize the worldwide waterway following its annexation of the adjoining Crimea Peninsula in 2014.
How Were EVMs Hacked? Here’s How It Allegedly Took Place in 2014
Addressing a press briefing on Monday, he claimed he could demonstrate how the voting machines can be hacked. He further said, "They are making a hacking horror show of their possible defeat in the upcoming elections".
New Zealand contributed three of the top-five batsmen to the test XI, with Sri Lankan opener Dimuth Karunaratne partnering Latham at the top, and Kohli listed at four in between Williamson and Nicholls.
New Zealand played just seven tests with Latham and Nicholls each scoring 658 runs after their December gorge against Sri Lanka, and Williamson 651.
Senior statesman Ross Taylor averaged 91 across 10 ODI innings past year, and was a shoo-in for the ICC one-day team.
Afghanistan leg-spinner Rashid Khan was runner up to Kohli for the ICC ODI Player of the Year award.
The 21-year-old Pant was picked by the ICC's voting academy for a stellar show in his breakthrough Test year in 2018.
India head into the series on the high of a historic series in Australia leveling the T20I series 1-1, winning the Test series 2-1 and finally claiming their first-ever bilateral ODI series win in the country with a 201 margin. Shankar joined the team ahead of India's second ODI against Australia, while Gill will join the team that is to fly to New Zealand.
ICC ODI Team of the Year 2017-18: Rohit Sharma (IND), Jonny Bairstow (ENG), Virat Kohli (captain) (IND), Joe Root (ENG), Ross Taylor (NZ), Jos Buttler (wicketkeeper) (ENG), Ben Stokes (ENG), Mustafizur Rahman (BAN), Rashid Khan (AFG), Kuldeep Yadav (IND), Jasprit Bumrah (IND).