This Rosh Hashana, which falls on Thursday, celebrates the start of year 5768 on the Jewish calendar.
"The sound of the Shofar heralds the beginning of a new year and a time of remembrance and renewal for the Jewish people," Bush wrote.
In his greeting Bush expressed hope for the future and stressed the power of faith, tradition and family values. "During these holy days, men and women are called to reflect on their faith and to honor the blessings of creation.
"The enduring traditions of Rosh Hashanah remind us of the deep values of faith and family that strengthen our Nation and help guide us each day.
"As Jewish people around the world come together to celebrate Rosh Hashanah, it is a chance to look to the new year with hope and faith," Bush concluded.
The message was signed by both the president and first lady Laura Bush.