Aaron Hernandez wrote a pen pal a letter from inside his jail cell, declaring his innocence, saying his murder charges are God's plan, and vowing to return to the NFL ... and TMZ has a copy.

We have verified with law enforcement the

is the real deal. You can read it yourself ... among the highlights:

-- "The world just makes things out of false accusations ... and it will all die down, especially when they say NOT GUILTY"

-- "All the people who turned on me will feel like crap."

-- "God put me in this situation for a reason."

-- "Can't wait to sign [autographs] again when I'm playing again an [sic] prove all the haters WRONG."

As for the fan who received the letter, Karl ... he just called in to "TMZ Live" and told us he wrote Hernandez first.

Play video content

Karl says he sent the letter because he was in the same jail 15 years ago, and wanted to reach out to Hernandez to give him some encouragement.

Karl also says he would like to visit Aaron in jail -- if Aaron will let him.