Tripp Easton Mitchell Johnston was born to Bristol Palin and her boyfriend Levi Johnston on December 27.
"The road ahead for this young couple will not be easy, but nothing worthwhile is ever easy," the statement by the newborn's governor-grandmother said.
Bristol Palin's teen pregnancy was revealed shortly after her mother was confirmed as John McCain's running mate in August, and quickly became a campaign talking point.
Sarah Palin, a devout Christian who is vehemently opposed to abortion, always put a positive spin on her daughter's pregnancy, but in the statement issued this week, she admitted to feeling fear and despair on learning she was to become a grandmother.
"When Bristol and Levi first told us the shocking news that she was pregnant, to be honest, we all at first looked at the situation with some fear and a bit of despair," Palin said in the statement.
"Isn't it just like God to turn those circumstances into such an amazing, joyful blessing when you ask Him to help you through?" she said.
In the same statement, Bristol Palin said becoming a teen mother was "not ideal" and spoke out against teen pregnancy.
"Teenagers need to prevent pregnancy to begin with -- this isn't ideal," she said before thanking her "supportive family which is dealing with this together."
Bristol Palin, now 18, will return to high school next week to earn the final credit that she needs to graduate, according to the statement. It was unclear if she intended to pursue a higher education on completing high school.
The baby's father will finish high school online while continuing to work as an electrical apprentice, the statement said.
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Image of Sarah Palin by William Thomas Cain