* Total cloud revenue up 58.4 pct in fourth qtr
* Forecasts Q1 EPS between 59-61 cents vs est 59 cents
* Shares rise 10.6 pct after-market (Adds executive and analyst comment, current-quarter forecast; updates shares)
June 21 (Reuters) - Oracle Corp's quarterly profit blew past Wall Street estimates and the business software maker forecast an upbeat current-quarter earnings, indicating that the company's transition to cloud is starting to pay off.
The company's shares were up 10.6 percent to a record high of $51.25 in after-market trading on Wednesday. They had gained about 20 percent this year.
A late entrant to the cloud market, Oracle has been doubling down on efforts to bolster its cloud-based services as customers increasingly shun the costlier licensing model.
As part of the efforts, the company and AT&T Inc signed in May a deal under which the U.S. telecom provider agreed to move some of its large-scale databases to Oracle's cloud platform.
"In the coming year, I expect more of our big customers to migrate their Oracle databases and database applications to the Oracle Cloud," Oracle founder and Chief Technology Officer Larry Ellison said in a statement.
Total cloud revenue surged 58.4 percent to $1.36 billion in the fourth quarter ended May 31.
"After several years of struggling to find its footing in cloud, Oracle seems to have turned the corner and heads into its fiscal 2018 with significant momentum," said Josh Olson, analyst at Edward Jones.
The success in the cloud business was highlighted by company executives on a post-earnings call.
"We sold more than $2 billion in cloud annually recurring revenue. This is the second year in a row that we sold more cloud ARR than Salesforce.com," Ellison said on the call.
Buoyed by the growth in cloud, the company forecast first-quarter adjusted profit of between 59 cents and 61 cents per share on a constant currency basis, while analysts' were expecting 59 cents.
On a constant currency basis, Oracle said it expected revenue to grow between 4 percent and 6 percent in the current quarter.
To increase its competitiveness in the cloud market, Oracle has also acquired companies including NetSuite, its largest purchase to date.
Meanwhile, Oracle's hardware revenue declined 13.2 percent to $1.11 billion and new software licenses fell 5.1 percent to $2.63 billion in the latest quarter.
Net income rose to $3.23 billion, or 76 cents per share, in the fourth quarter, from $2.81 billion, or 66 cents per share, a year earlier.
Excluding items, Oracle earned 89 cents per share.
The company reported an adjusted revenue of $10.94 billion.
Analysts on average had estimated a profit of 78 cents per share and revenue of $10.45 billion, according to Thomson Reuters I/B/E/S.
(Reporting by Pushkala A and Laharee Chatterjee in Bengaluru; Editing by Arun Koyyur and Sriraj Kalluvila)