Taylor, 30, who is set for a hero's welcome when he returns to his hometown of Prestonpans, East Lothian, has also revealed that the first thing he will do on landing back in Scotland is thank Ken Buchanan.
Until the early hours of Sunday morning, Buchanan, currently in an Edinburgh care home, had been the only Scots fighter to become undisputed world champion.
Taylor equalled that feat by beating Jose Ramirez by unanimous decision in Las Vegas in a pulsating light-welterweight unification bout.
Now undefeated in 18 bouts, two thumping left hands from The Tartan Tornado put the American down and ensured a 114-112 score.
Having become only the fifth man in boxing to hold all four belts in a division, the Hibs fan has set his heart on fighting in front of a home crowd.
Speaking afterwards, Taylor said: “I’ve not boxed in my home city for a few years so I would love to take a big fight back to Scotland.
“Now is the time to get that fight at Edinburgh Castle or Easter Road.”
The slice of history the Scot has carved out for himself has been hailed by supporters.
Shaz Shafiq, of SWT SCNC Apparel, which has sponsored Taylor since he turned professional in 2015, insists the boxer has earned the right to be recognised alongside other sporting greats.
He said: “He’s made history for Scotland and put Scotland back on the map, especially for boxing.
“We’ve always had good boxers: the likes of Alex Arthur, Ricky Burns, Scott Harrison and Ken Buchanan – you can’t forget him – but what Josh has done probably exceeds all of them.
“It’s just another level. We’ve known him since he was an amateur at Lochend Boxing Club. Josh is a lovely lad.
“He’s down to earth and he’s always got his feet on the ground so, even now, he’ll take time out to speak to people.
“He’s just a normal guy and all his family are brilliant. I hope he gets what he deserves and gets some big fights, hopefully back in Vegas, so the supporters can all go over.”
Taylor’s partner, Danielle Murphy, tweeted: “My man is the undisputed world champion, just saying.
“Thank you so much to everyone for your well wishes and support! It honestly means the world to us! You are all the best.”
Councillor John McMillan, Provost of East Lothian, said: “To be crowned the undisputed world champion is a fantastic achievement for Josh Taylor and one which reflects a massive amount of hard work, commitment and determination over the years.
“He has demonstrated a real will to win. I know that so many people, across East Lothian and further afield, were rooting for Josh. Huge congratulations on this historic achievement.”
Addressing the possibility of hosting a Taylor match, a Historic Environment Scotland spokeswoman said: “Edinburgh Castle esplanade is an iconic and sought-after venue for a range of different events, which are considered on a case-by-case basis.
“A proposal and business case would need to be submitted before we could determine if an event could go ahead, due to the challenging logistics involved.”