The International Fellowship of Christians and Jews, the charity he founded over 35 years ago, said Eckstein, 67, died at his home in Jerusalem. Local media said he died of heart failure.
The U.S.-born Eckstein founded the fellowship in 1983, befriending evangelical leaders in the U.S. and building support for Israel. Eckstein said his decades of efforts helped make support for Israel a top priority in the evangelical world.
"After 2,000 years of oppression and persecution, today you have Christians who are helping Jews," he told The Associated Press last year. "This is an amazing thing."
Over the years, the group raised over $1.5 billion, according to its website. Most of that money came in small amounts from individual Christian donors.
Eckstein became a well-known figure in Israel, funding projects for children, new immigrants, Holocaust survivors, orphans, the elderly and victims of Palestinian violence. His group also assisted distressed Jewish communities in places like Ethiopia and the former Soviet Union.
His face frequently appeared in large posters promoting his work, and his voice, instantly recognizable for its thick American accent, was often heard in radio advertisements.
At times, Eckstein drew criticism from some quarters. Liberal American Jews sometimes objected to his ties with the conservative Christian right and his group's activities in West Bank settlements. In Israel, some saw the reliance on foreign Christian groups for financial assistance as inappropriate.
Israeli Prime Minister Benjamin Netanyahu expressed "deep sorrow" over Eckstein's passing, saying he "worked tirelessly to benefit the citizens of Israel and to strengthen the bond between Christian communities and the State of Israel."
Singer Pat Boone called Eckstein's death "a tremendous and personal shock to me," saying he had worked with the rabbi over the years to raise money from Christians for the support of Israel.
"I will always consider my friendship and cooperative work with Yechiel Eckstein one of the most important facts of my life on this earth — and I hope to rejoice with him in Heaven, the ultimate Promised Land," Boone said in a statement.
Eckstein is survived by his wife, Joelle, three daughters and eight grandchildren, according to his group's website.