Mentioning previous AskHistorians answers is not intended to discourage questions, especially because archived posts can't be replied to (and new comments would tend to get ignored anyway), and some of these comments didn't address the "without significant opposition" part of the question.

The most pertinent article seems to be this from the FAQ: "Was there notable opposition to allowing James VI to ascend to the English throne", comments by /u/historiagrephour. They concluded with,

TL;DR? The English had a choice between James and two unmarried, childless women. They were tired of women rulers who might or might not provide an heir and because James had already fathered kids, they knew that the succession was safe should he suddenly kick the bucket. Moreover, James was a Protestant when one of the female claimants was Catholic, and James had already been a monarch for thirty-six years by the time he succeeded in England. He knew what he was doing whereas the women didn't. So, the English were like 'Eh, could be worse. He might be Scottish, but at least he's not a woman.'

If you care about the propaganda of the time, GeneralLeeBlount pointed to the proclamation of 1604.

For a bit more information on Mary Queen of Scots, there was "How did Queen Elizabeth I go from being hell-bent on killing Mary, Queen of Scots to naming her son James as her successor?", answered by /u/neverwasahat (a Best Of for April 2017).

For more info about other candidates, "Succession of Queen Elizabeth I and possible candidates.", answer by /u/RTarcher.