The double Olympic champion posted an emotional message on social media saying he was "heartbroken" over the death of his friend.
The five-time NBA champion and two-time Olympic gold medallist and his 13-year-old daughter Gianna were killed in a helicopter crash on Sunday.
"I'm not ready but here I go. Man I sitting here trying to write something for this post but every time I try, I begin crying again just thinking about you, niece Gigi and the friendship/bond/brotherhood we had!," James posted on social media.
James and Bryant won Olympic gold together for Team USA at Beijing 2008 and London 2012. Just one day before the tragic accident he passed Bryant to become the third highest scorer in NBA history.
"I literally just heard your voice Sunday morning before I left Philly to head back to LA. Didn’t think for one bit in a million years that would be the last conversation we’d have."
"I’m heartbroken and devastated my brother! Man I love you big bro. My heart goes to Vanessa and the kids. I promise you I’ll continue your legacy man!"
"You mean so much to us all here especially #LakerNation and it’s my responsibility to put this on my back and keep it going! Please give me the strength from the heavens above and watch over me! I got US here!
There’s so much more I want to say but just can’t right now because I can’t get through it! Until we meet again my brother!"
The two never played together in the NBA, but were teammates when the US national team clinched two Olympic titles.
Incidentally, Bryant's final social media post was a congratulatory message to James, after he surpassed him in the all-time scoring list.
James passed his mark of 33,643 points in Saturday's game that the Lakers lost to the Philadelphia 76ers.
The NBA has called off the Los Angeles Lakers game against the LA Clippers scheduled for Tuesday, 28 January.
The NBA said, "the decision was made out of respect for the Lakers organisation, which is deeply grieving the tragic loss of Lakers legend Kobe Bryant, his daughter Gianna and seven other people in a helicopter crash on Sunday."