Buck, 24, was one race away from being left out by UK Athletics head coach Charles van Commenee but fulfilled the selection criteria less than 24 hours before the closing date on February 21.
Buck had won 400m silver in the UK Indoor Trials and Championships in 47.13secs, well outside the standard of 46.70.
The sprinter then recorded 46.77 in finishing fourth at the Aviva Grand Prix a week later but, with time running out, Buck raced at the Midlands Open the following day, storming to a time of 46.38.
“Hopefully I can go to the Europeans in good form now because I want to be pushing for a medal in Paris – that has been the aim all along,” said Buck.
“I was really pleased with the time I ran at the Midland Open and it reflected the form I expected to be in during the indoor season.
“I was disappointed after the trials. The final was a really hard race and I got cut up and then I had to cut someone else up – it was pretty typical of an indoor race.
“I felt I left something in the tank but I did think I would still get the time for the Europeans in Birmingham and I wasn’t too worried.
“But after I didn’t, I was so relieved that all the training finally came together.
“It all came down to the last day really and that time at the Midlands Open.”
Buck will begin his campaign this morning with the heats of the 400m before ending it on Sunday evening with the 4x400m relay.
He joins Nick Leavey, Luke Lennon-Ford, Nigel Levine, Leeds-born Richard Strachan and Conrad Williams as part of a six-strong relay squad.
To watch British athletes in action at the Aviva Series go to www.aviva.co.uk/athletics.