According to Wikipedia, they're traced to a 4th century monk, Evagrius Ponticus, whose work was reinterpreted by Pope Gregory I in AD 590 to become the commonly accepted 7 deadly sins.
Wikipedia - Seven deadly sins
A specific list of the 7 cannot be found in the Bible, but I expect they're biblical sins nonetheless.
Cruelty is sinful, in that it's derived from hate.It's a shame that cruelty isn't included in the list.
The seven deadly sins, like most medieval concepts, are absurd.
Gluttony isn't mentioned at all in the Bible. To the contrary, if you have a lot of food, it's because God has blessed you.
Sloth sure isn't a sin. It can actually be quite productive to do nothing for a while and take a rest.
Proverbs 23:20-21 warns us, “Do not join those who drink too much wine or gorge themselves on meat, for drunkards and gluttons become poor, and drowsiness clothes them in rags.” Proverbs 28:7 declares, “He who keeps the law is a discerning son, but a companion of gluttons disgraces his father.” Proverbs 23:2 proclaims, “Put a knife to your throat if you are given to gluttony.”
Physical appetites are an analogy of our ability to control ourselves. If we are unable to control our eating habits, we are probably also unable to control other habits, such as those of the mind (lust, covetousness, anger) and unable to keep our mouths from gossip or strife. We are not to let our appetites control us, but we are to have control over our appetites. (See Deuteronomy 21:20, Proverbs 23:2, 2 Peter 1:5-7, 2 Timothy 3:1-9, and 2 Corinthians 10:5.) The ability to say “no” to anything in excess—self-control—is one of the fruits of the Spirit common to all believers (Galatians 5:22).
Proverbs 6:6–11
6 Go to the ant, O sluggard; consider her ways, and be wise. 7 Without having any chief, officer, or ruler, 8 she prepares her bread in summer and gathers her food in harvest. 9 How long will you lie there, O sluggard? When will you arise from your sleep? 10 A little sleep, a little slumber, a little folding of the hands to rest, 11 and poverty will come upon you like a robber, and want like an armed man.
Proverbs 10:4–5
4 A slack hand causes poverty, but the hand of the diligent makes rich. 5 He who gathers in summer is a prudent son, but he who sleeps in harvest is a son who brings shame.
Proverbs 10:26
Like vinegar to the teeth and smoke to the eyes, so is the sluggard to those who send him.
Proverbs 12:24
The hand of the diligent will rule, while the slothful will be put to forced labor.
Proverbs 12:27
Whoever is slothful will not roast his game, but the diligent man will get precious wealth.
Proverbs 13:4
The soul of the sluggard craves and gets nothing, while the soul of the diligent is richly supplied.
Proverbs 15:19
The way of a sluggard is like a hedge of thorns, but the path of the upright is a level highway.
Proverbs 19:15
Slothfulness casts into a deep sleep, and an idle person will suffer hunger.
Proverbs 19:24–25
24 The sluggard buries his hand in the dish and will not even bring it back to his mouth. 25 Strike a scoffer, and the simple will learn prudence; reprove a man of understanding, and he will gain knowledge.