The 22-year-old from Bristol was shot during an insurgent attack in Nahr-e Saraj, Helmand Province, on 14 August.
He later died in Queen Elizabeth Hospital, Birmingham, on Friday.
The father of one joined the Army in 2009 and deployed to Afghanistan for the first time on April 5 this year.
‘A great soldier’
His family said: “Karl was one in a million. He was a proud and caring man who took pride in whatever he did.
“The family are obviously devastated. Karl was the light of many lives and touched all who knew him.
“He will be especially missed by his baby daughter Grace, who has lost her number one man.”
Lieutenant Colonel James Bowder, Commanding Officer of 1st Battalion Grenadier Guards, described Guardsman Whittle as “one of our very best. A great soldier and a young man of rare character, he was destined to go a very long way in the Army.
“Big, strong and full of fight, he battled hard against his injuries right to the very end. His loss has been keenly felt in a close Battalion, and our prayers are with his family at this most difficult of times.”
He added: “I am immensely proud of what Guardsman Whittle achieved out here in Afghanistan and more broadly during his military career.
“He was utterly committed to his fellow guardsmen, his company and the mission. He will never be forgotten by either the battalion or the broader regimental family.”