The Democrat, the last of the late John F. Kennedy's brothers, passed away aged 77 following a long battle with brain cancer.
Schwarzenegger, who is married to Kennedy's niece Maria, was devastated to hear the news - branding Kennedy "the rock" of the family whose "legacy will live on".
A statement from the star reads, "Maria and I are immensely saddened by the passing of Uncle Teddy. He was known to the world as the Lion of the Senate, a champion of social justice, and a political icon.
"Most importantly, he was the rock of our family: a loving husband, father, brother and uncle. He was a man of great faith and character. Teddy inspired our country through his dedication to health care reform, his commitment to social justice, and his devotion to a life of public service.
"I have personally benefited and grown from his experience and advice, and I know countless others have as well. Teddy taught us all that public service isn't a hobby or even an occupation, but a way of life and his legacy will live on."
U.S. President Barack Obama is also coming to terms with Kennedy's passing, insisting he and his wife Michelle were "heartbroken" to hear the sad news and has sent his condolences to his extended family.
Obama has credited his fellow Democrat with helping him win his race for Presidency earlier this year (Jan09) - and insists America has "lost a great leader".
He says, "Michelle and I were heartbroken to learn this morning of the death of our dear friend, Senator Ted Kennedy... I cherished his confidence and momentous support in my race for the Presidency. And even as he waged a valiant struggle with a mortal illness, I've profited as President from his encouragement and wisdom.
"An important chapter in our history has come to an end. Our country has lost a great leader, who picked up the torch of his fallen brothers and became the greatest United States Senator of our time. The Kennedy family has lost their patriarch, a tower of strength and support through good times and bad.
"Our hearts and prayers go out to them today - to his wonderful wife, Vicki, his children Ted Jr., Patrick and Kara, his grandchildren and his extended family."