He thanked all those who had taken part in the revolution – from rebel fighters to businessmen and journalists.
Mr Abdul Jalil bowed down to thank God for victory before making his speech.
“Today we are one flesh, one national flesh. We have become united brothers as we have not been in the past,” he said.
“I call on everyone for forgiveness, tolerance and reconciliation. We must get rid of hatred and envy from our souls. This is a necessary matter for the success of the revolution and the success of the future Libya.”
Mr Abdul Jalil said the new Libya would take Islamic law as its foundation. Interest for bank loans would be capped, he said, and restrictions on the number of wives Libyan men could take would be lifted.
US President Barack Obama congratulated Libyans, saying: “After four decades of brutal dictatorship and eight months of deadly conflict, the Libyan people can now celebrate their freedom and the beginning of a new era of promise.”