Muir had finished 11th in the 1,500m final in front of her home crowd at the 2014 Games in Glasgow and was unable to compete four years later on the Gold Coast due to her veterinary medicine exams.
"I think I would have said to the Laura Muir of 2014 'your time will come'," Muir, who won Olympic silver for Britain in Tokyo, remarked.
"It's rotten at the time but you learn from it and you come back stronger. This meant a lot to me - missing the Gold Coast (in 2018) as well, it's been bugging me for eight years."
Muir, who also won bronze in the 800m in Birmingham, clocked a time of four minutes, 2.75 seconds to take gold ahead of Northern Ireland's Ciara Mageean (30) and Australia's Abbey Caldwell (21) on Sunday.
"It is so nice to come here and not just get one medal but two and in such a competitive field," she added. "Those girls are fast. It means a lot."
