The first picture shows her and McCartney, 72, surrounded by a number of instrumentalists including Pearl Jam's guitarist Mike McCready, reported Aceshowbiz.
"Working on one of his many secret projects! Killer musicians, vibe, and lots of laughs," she wrote.
She and McCartney pose next to a drum kit in the second snap.
The 28-year-old 'Applause' singer revealed in the caption that she once 'rejected' a collaboration with the surviving member of The Beatles.
"Always a good time with my buddy. I'll never forget when he called me last year to work and I hung up the phone cuz I thought it was a prank!" she said.