There have been many changes to the draft over the years, one thing that hasn't seemed to change in a while is the number of rounds. It feels like it has almost always been 7, but it hasn't.
In the very first draft, in 1936, there were 9 rounds. The reason for nine was because no team had a scouting department at the time. The following year it was bumped up to 10 rounds. Then in 1939, it jumped all the way to 20 rounds. The draft expanded to 20 rounds in 1939 due to a plan proposed by Bert Bell, the owner of the Eagles and future NFL commissioner, in 1935. The plan said that teams would select players in reverse order of their finish the previous season
In the 1940s, there were as many as 32 rounds. A couple of years after merging with the AFL, the NFL reduced the number of rounds from 17 to 12 in 1977. The league would then continue to make some changes until 1993, which had 8 rounds. That led into the next year when they decreased it to have 7 rounds, and since then it's always been seven.
A big reason for the constant decrease in the number of rounds was actually so fewer players would be selected. In 1993, the modern-day free agency structure was put into place, and, in 1994, the NFL's salary cap was put into place. This restricted how much owners could spend on player salaries. So by lowering the rounds of the draft to lower the number of players drafted, it would actually benefit the players that go undrafted, compared to what would have happened if they got drafted in the 10th or 12th round. Undrafted players become free agents and have the power to sign with any team that offers them.
There have been numerous changes to the draft, especially in the number of rounds. But as more years go by, it seems that they believe 7 is the number that will stick.