The England team, who fly to Johannesburg to Harare early Friday for their 10-day, five-match tour, had been ready to pull out till early Thursday when certain members of the British media were finally granted accreditation.
In the huge market that is world sport, England and Wales Cricket Board (ECB) chairman Morgan said money was a prime factor in their thinking, particularly with the ever-present threat of fines from the International Cricket Council (ICC) if they withdrew from the tour for anything other than safety or security grounds.
"I have certainly looked at what's happening here. We have sympathy with the people here but the ECB is in business - our trade is cricket and the revenue part of our trade is international cricket," Morgan added.
"In order to trade internationally, we have to play by the rules of the ICC and the rules of ICC are such that member countries are not allowed to avoid tours as part of the Future Tours Programme for moral reasons."
Morgan also admitted it would a difficult situation if he was asked to shake hands with president Mugabe.
Mugabe may turn up at one of the One-day matches in his role as patron of the Zimbabwe Cricket Union.
Morgan insisted he had received advice about what to do if the situation arose.
"The Foreign Secretary (Jack Straw) has in recent times shaken the hand of Mr Mugabe. It will be a difficult call. I've had confidential advice from the Foreign Office and that advice will be uppermost in my mind," he said.
Morgan defended the decision to press ahead with the tour and insisted he had "accomplished his mission" in ensuring accreditation was granted to British journalists covering the tour.
Zimbabwean authorities initially barred 13 journalists from having accreditation on political grounds.
At one stage the whole tour seemed in doubt when Morgan told the team to remain in South Africa until the row was resolved, with the ICC apparently backing the ECB's stance.
However the tour is now going ahead after the Zimbabwean government granted admission to the journalists they had originally barred, though it seems set to be a four-match rather than five-match series after the game scheduled to be played on Friday was cancelled.
The tour will now start with the second scheduled match in Harare on Sunday.
The players are said to be angry at the farce that has ensued, but Morgan stood by the work he has done on the ECB's behalf this week.
"We came here (to Harare) on Wednesday with the mission of gaining accreditation for 13 journalists and that mission was accomplished yesterday," he told BBC Radio 5 Live.