There are numerous versions of Apple's own browser on App Store, but Norway-based Opera is the first rival to get access to iPhone.
Shares in Opera rose 5.7 percent at the open, to 26.2 crowns.
Opera applied on March 23 for its mobile browser to be distributed on iPhone, and it was available for downloading to consumers early on Tuesday, three weeks later. Usually the review process takes up to one week, developers say.
Analysts have said the decision was difficult for Apple -- whose application store is the only way to distribute software for iPhone users -- as its Internet browsing function is key to the success of the iPhone.
In this world you have to be careful in picking your fights, said John Strand, chief executive of Strand Consult. Apple has to know Opera is the company that won the big legal battle against the Microsoft browser and probably didn't want to fight against Opera, Strand said.
Opera led the battle in Brussels against Microsoft bundling its Windows software and Internet Explorer, which eventually saw Microsoft sending a browser choice screen to some 200 million computers in Europe.
Opera's browser promises up to six times faster download speeds than Apple's own browser, and to cut data traffic by up to 90 percent.
Massive data traffic from iPhone mobile phones has caused problems for many operators' networks.
Analysts said iPhone access should have little direct business impact for Opera, but was important for branding.
Opera's Mini browser already has some 50 million users and this could give them a couple or more million ... but it is important to bear in mind that they don't make money on users that download Opera Mini for free, analyst Peder Strand at SEB Enskilda said.
Opera's browser, free to consumers, was among the top downloaded items on iPhone on Tuesday.
We have the same business model on Opera Mini as on our other consumer products, which is revenue share and affiliate deals on search and speed dials, Opera's Chief Development Officer Cristen Krogh told Reuters.
(Additional reporting by Richard Solem in Oslo; Editing by Lincoln Feast and Rupert Winchester)