His campaign strategy was to lure working-class Democrats to his cause, just the way Reagan did. That Reagan had already lured them was incidental; Trump insisted that he would engender the love of those blue-collar voters and win because of them.
He sort of did.
Trump's depiction of who those voters were centered on two broad archetypes: Veterans and displaced factory workers. There isn't good polling on the former, but it overlaps with the white, non-college-educated men who made up a significant part of Trump's base. In one formulation of the latter, union members, we have data from exit polling. In union households (that is, households in which someone was a union member), Trump trailed Hillary Clinton by only 8 points, a substantial improvement from how Mitt Romney did in 2012.
In fact, it was the best margin for a Republican since ... 1984, the election that gave Reagan his second term.
Exit poll data can be iffy, but this matches polling from earlier this year. That's the good news that Trump will want to trumpet. But it's more complicated than that.
It's not clear, generally, that "union household" voting is equivalent to "union member" voting. A 2003 study found that about half of those who live in union households are actual union members. Anecdotally, non-union members living in union households tend to vote more like everyone else than like union members.
Update: To that point:
What's interesting about these numbers, though, is that Trump probably did better than Reagan with that core group of white union members. Why? Because the demographics of union membership have shifted a lot over the last 30 years.
According to the most recent data from the Bureau of Labor Statistics, white men still make up a plurality of union members. In the year 2000, 7.9 million white men were union members of 16.3 million total. By 2015, the number of union members had fallen to 14.8 million, and the number of white men in unions to 6.2 million. That's a drop in density from 48.4 percent to 41.9 percent -- just over the last 16 years.
That means that Trump did as well as Reagan in 1984 despite more of those union members being nonwhite. One reason why may be women who are members of unions. In 2012, Mitt Romney beat President Obama by 20 points among white women without college degrees. Trump beat Clinton with that group by 28 points.
These are Reagan's reelection numbers, mind you, which are down a bit from his numbers in 1980. We shall see whether or not Donald Trump will maintain this level of support if and when he runs for reelection, as the demographics of union membership continues to shift in a way that will likely not be helpful to him. But the headline has "Reagan" and "Trump" sitting next to each other, so he'll probably be content as it is.