“There is growing evidence that the iPhone is making inroads into the Enterprise,” writes Deutsche Bank research analyst Chris Whitmore in a report to clients Monday.

According to his estimates, Apple (AAPL) by the end of the year will have shipped about 2 million iPhones into corporate accounts through various routes, including internal IT department purchases and formal reimbursement policies.

That would give Apple about a 7% share of the enterprise smartphone market this year, up from 2% in 2008.

IT departments were famously resistant to the iPhone when it was launched two years ago. That resistance has begun to melt, writes Whitmore, for several reasons:

• User satisfaction. He cites the recent J.D. Power survey that named the iPhone “best in class” for both the consumer and enterprise markets
• Virtual keyboard. The initial perception that physical keyboards are critical for enterprise users has proved to be a “fallacy,” says Whitmore.
• Enterprise applications. Among the 95,000 apps available for the iPhone, Whitmore estimates that 6,000 are enterprise-related, illustrating what he calls the “accelerating utility of the platform.”
• Sluggish competition. The incumbents, Research in Motion (RIMM) and Microsoft (MSFT) Windows Mobile, with >60% and 20% enterprise share, respectively, “are years behind Apple,” he writes, “and appear to be losing ground in Developer support / Application development.”

See also:

• J.D. Power: iPhone is No. 1, again
• Top 10 reasons IT won’t support the iPhone
• Forrester: Top 4 reasons IT should support the iPhone

[Follow Philip Elmer-DeWitt on Twitter @philiped]