The batsman, who is ranked third in the world, delayed his departure to be with his partner Carrie for the arrival of their first child but will not be taking an extended paternity period following the safe arrival on Saturday.
Instead, Pit is believed Root will be joining his team-mates in Mumbai on Thursday and will travel with the squad to Pune ahead of Sunday’s first ODI.
Root is understood to have been keen to travel and did not request to skip the limited-overs leg of the trip, which consists of three 50-over games and three Twenty20s between January 15 and February 2.
England captain Eoin Morgan said: “He (Root’s son) and his wife are healthy which is great news and Joe should be ready for selection for the first ODI, which is also great news.”
Root is a first-choice player across all three formats and needs to have his workload managed as a result but Morgan insisted his new family circumstances did not alter England’s thinking on this occasion.
“We always consider that because Joe is first on the list to be rested if there is an opportunity,” said Morgan.
“We feel given this is a short series and we have three weeks at home before the West Indies tour, that the lead in to our summer is pretty casual really when you look at the international calendar and the opportunity for him to rest.
“So there’s always the debate and we feel at the moment there’s enough rest between now and the Champions Trophy for him to feel fresh at the start of June.”
While Root has already taken on one new position of responsibility in his personal life, there has been no news on whether or not he will soon be taking on an another on the pitch.
Yorkshireman Root scored 491 runs in the Test tour of India at the end of last year but a comprehensive 4-0 defeat saw calls for captain Alastair Cook to hand over the baton to his deputy.
England players and management have been firmly behind Cook continuing, in public and in private, but having said at the conclusion of the series he would take time to mull over his options, speculation continues.
A post-series debrief with the ECB’s managing director - and his long-time opening partner - Andrew Strauss, will take place this month but there is no guarantee Cook will deliver his verdict then.
With no Test cricket until July, the 32-year-old may defer his decision further and he ponders continuing after more than four years in the job.