The deal will help Europe's most valuable tech firm strengthen its customer relationship management (CRM) software offering, a focus of Chief Executive Bill McDermott in a race with CRM specialist Salesforce and arch-rival Oracle.
Announced late on Sunday, the deal is SAP's largest acquisition since it bought travel and expense-management firm Concur for $8.3 billion in 2014.
One person involved in the deal said it was the largest-ever takeover of a technology company on the verge of a market debut.
Qualtrics captures and analyses data on brands and products from real-time sources including social media and email, and should give SAP's clients better insights into their own customers' experience.
SAP's core strength lies in helping some of the world's biggest firms run their finance, logistics and human resources operations.
"Experience data plus operational data are a powerful combination," McDermott told reporters on a call. "This is the most pristine asset in the business software industry."
Shares in SAP fell 4.2 percent by 0910 GMT as traders and analysts believed SAP was overpaying.
"Might be a valid strategic rationale and top-line growth is impressive, but it's still expensive," said one trader.
McDermott said that once the deal closed SAP would achieve the fastest revenue growth of any company in the enterprise application software industry.
Revenue would grow by double digits, while non-IFRS operating income would outpace revenue, he said. SAP will update its guidance after the deal closes, which is expected in the first half of 2019.
Baader Helvea analyst Knut Woller said that at 21.5 times trailing annual revenue, the price SAP was paying is nearly double the multiples in comparable recent deals of 11.2 times. Woller has a "buy" recommendation on SAP shares.
Qualtrics expects revenue to exceed $400 million this year, and projects a growth rate above 40 percent, not including potential synergies that might arise from being part of SAP. It has 9,000 customers, mostly in the United States.
SAP expects its own revenue to grow this year by 7.5 to 8.5 percent to more than 25 billion euros.
Bernstein analyst Mark Moerdler, who rates SAP "outperform", said the acquisition would fill a void in SAP's portfolio.
"While SAP has paid premium prices for their acquisitions they have acquired quality assets and have been overall successful acquirers. We see this acquisition as incrementally positive for our thesis," he wrote in a note.
Moerdler also noted that the acquisition would make SAP more of a competitor to Adobe, with whom it recently announced a customer data-sharing initiative along with Microsoft, in experience management and e-commerce.
SAP will acquire all of the outstanding shares in Qualtrics and has secured 7 billion euros in financing to cover the purchase price and acquisition-related costs for the deal, which has been approved by both companies' boards.
Qualtrics CEO Ryan Smith, who owns about 40 percent of the 16-year-old company with his brother and father, will stay on and the company will retain its dual headquarters in Provo, Utah, and Seattle.
Smith told Reuters that the IPO would have valued the company at least at $6 billion.
"We were going to be one day worth $20 billion or $30 billion, like a ServiceNow Inc or a Workday Inc," Smith said. "We were under no financial pressure to do anything."
Smith said the business had been consistently cash-flow positive since it was founded in his parents' basement.
McDermott said he and Smith met a few months back and quickly struck up a friendship: he said he arrived for lunch one day at Smith's home in a suit and dress shoes, and the two ended up playing basketball in the yard.
"We hit it off right off the bat," said McDermott, a 57-year-old New Yorker who has headed SAP since 2010.
The SAP boss had previously said he was only looking at "tuck-in" acquisitions. He described the Qualtrics deal as transformational in terms of growth potential, comparing it with Facebook Inc takeover of photo-sharing site Instagram.
Qualtrics was advised on the transaction by Qatalyst Partners and Goodwin Proctor, LLP. JPMorgan acted as financial adviser and Jones Day as legal adviser to SAP.
(Reporting by Douglas Busvine in Frankfurt and Liana B. Baker in New York; additional reporting by Helen Reid in London; editing by Kirsten Donovan, Georgina Prodhan and Adrian Croft)
By Douglas Busvine