The register which keeps track of the execution of a program and which contains the memory address of the instruction currently being executed is known as

Program counter : A program counter is a register in a computer processor that contains the address (location) of the instruction being executed at the current time. As each instruction gets fetched, the program counter increases its stored value by 1. After each instruction is fetched, the program counter points to the next instruction in the sequence. When the computer restarts or is reset, the program counter normally reverts to 0.

Source : techtarget.com