Botha, 25, will move to the province in the summer on the conclusion of the Super Rugby campaign.
The forward, who has been capped twice by the Springboks, can operate as either a flanker or number eight.
Connacht scrum-half John Cooney is also joining Ulster and will replace crowd favourite Ruan Pienaar who is being forced to leave in the summer.
Cooney, 26, has penned a two-year deal and fulfils the IRFU directive that Ulster sign an Irish-qualified scrum-half to take over from South African Pienaar.
Botha has played 46 times for the Bulls, whose High Performance Manager admitted could not compete with the financial package tabled by the Irish province.
"Arno received a very good offer from Ulster," said Janse van Rensburg.
"The situation is that we can't financially make an offer close to what he's currently earning."
The player is looking forward to a new challenge.
Botha stated: "the decision to move to Ulster was taken after considerable thought from my side and I feel it is the right time in my career to feel what rugby in the northern hemisphere is all about".
On Botha's arrival, Ulster's Director of Rugby Les Kiss said: "he is an ambitious young man and he is determined to make an impact with us, he is a serious competitor".
The South African made his international debut against Italy in 2013 but suffered a knee injury just four minutes into his second test against Scotland.
He returned to full fitness and captained the Blues to the final of last year's Currie Cup.
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"Arno was tipped to be a future Springboks captain from a young age but his career was somewhat curtailed by injuries," said Kiss.
"Those injuries are behind him now and he has regained his best form over the past 12 months.
"He is very aggressive in attack and his ability to get over the gainline will be especially good for us.
"Arno is also strong in defence, he's a nuisance at the breakdown and he's a good lineout option, so he has a very well-rounded game."
South African Marcell Coetzee, who joined Ulster last summer, is due to make his debut in next month's Pro12 game against Edinburgh having recovered from a long-term knee injury.
Ulster's defeat by Exeter Chiefs on Sunday ended their qualification hopes in this season's European Champions Cup. The province is currently sixth in the Pro12 table.
Further changes to the coaching staff and playing personnel are expected, with Kiss indicating more news signings will be made in the coming weeks to bolster the squad for next season.
South African back row forward Arno Botha is joining Ulster on a two-year deal from the Blue Bulls.