The family's letter reads: "Our beloved Tim was a seeker, a fragile artistic soul who always carried great existential questions.
"An overperforming perfectionist who travelled and worked hard at a tempo which led to extremely difficult stress.
"When he stopped touring, he wanted to find a balance in life to feel good and be able to do what he loved the most - music.
"He truly battled thoughts about the Meaning, Life, Happiness.
"Now, he could not go on any more. He wanted peace.
"Tim was not made for the machinery he ended up in, he was a sensitive guy who loved his fans, but shunned the spotlight," the statement read.
"Tim, you will forever be loved and missed. Who you were and your music will carry on the memory of you.
"We love you, the family."
The family's heartbreaking letter comes as a choir of 1000 singers paid tribute to the Swedish DJ during a concert in his home town of Stockholm, performing his hit Wake Me Up.
A video of the performance was posted by the Happy Voices' choir leader Gabriel Forss, following the concert in Filadelfiakyrkan in central Stockholm.
He wrote: "A tribute to Avicii from last night's concert in Stockholm. A thousand singers from my choir Happy Voices performing Wake Me Up.
"Thank you Tim. Your music will forever bring people together."
Despite a meteoric rise to success following the release of hit-single Le7els in 2011, Avicii announced in 2016 that he would not longer perform live, following years health problems caused by stress and alcohol abuse, as well as severe anxiety.
A recent documentary, Avicii: True Stories shed light on the extreme pressure he was under, performing 320 shows in a single year.
In the documentary, Avicii, a self-confessed introvert, speaks frequently about using alcohol as a crutch to be able to perform, drinking every day during his hectic tour, and to help him with his crippling anxiety and stress.
At the age of 21 he was diagnosed with acute pancreatitis - a potentially life-threatening inflammation of the pancreas - due in part to excessive drinking.
In 2014, Bergling was again hospitalised and forced to have his gallbladder and appendix removed.
Avicii made a fortune during his short career, cashing in $28million in 2014 alone, earning US$250,000 a night when playing out sold-out shows, according to GQ.
Avicii himself was less bothered about his millions, saying in 2013 that he "noticed straight away when I started making money, that I don't need that much money".
In 2012 he donated the entire income of his US tour - more than one million dollars - to hunger relief charity Feeding America, and in 2013 he gave one million euros to Swedish aid organisation Radiohjรคlpen.
Bergling grew up in affluent Ostermalm in the Swedish capital Stockholm, and began producing music in high school.
He made a name for himself on the EDM (Electronic Dance Music) scene, before his breakthrough hit Le7els in 2011.
He would later become known for hits like Wake Me Up!, You Make Me, and recently Lonely Together, a collaboration with Rita Ora.
He won two MTV Music Awards, one Billboard Music Award and earned two Grammy nominations.
Just three days before his death, in his final post on Twitter, Bergling thanked the Billboard Music Award's jury for his nomination int the Top Dance/Electronic Album category for his EP Avฤซci (01).
He died on April 20 in Muscat, Oman, where he is reported to have been holidaying with friends.
The cause of death has not been made public.
Where to get help:
โข Lifeline: 0800 543 354 (available 24/7)
โข Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
โข Youthline: 0800 376 633
โข Kidsline: 0800 543 754 (available 24/7)
โข Whatsup: 0800 942 8787 (1pm to 11pm)
โข Depression helpline: 0800 111 757 (available 24/7)
If it is an emergency and you feel like you or someone else is at risk, call 111.