Both deny the charge, and Monday's hearing was the jury's first chance to hear directly from one of the defendants about what led to the attack.
Adebolajo laid out his life story, saying his parents were Christian and he used to read from the Bible, but he became frustrated and converted to Islam during his time in university.
He said he had tried to travel to Somalia so that he could live under Sharia law, but was detained by Kenyan troops before he could get there.
Turning to the attack, he said that he tried to make sure that Rigby was a soldier before he killed him, saying he hoped the death could “indirectly save the lives of many.”
“I was keen that the reason for the death of this man is not misunderstood. I wanted people to understand ... It only happened for one reason only, and that is foreign policy,” he said.
Adebolajo said he rushed at the police who arrived at the scene minutes after the killing because his religion forbade him to run away from the enemy.