He believes the iPhone 7 turned out to be substantially better than everyone was expecting.
"We view the phone to actually be a pleasant surprise. Many of the features had been leaked, but the extra battery life, the performance, the additional speakers were a nice surprise," he said.
He has a "buy" rating on the stock and a $130 price target.
Apple launched the new phones last week and said Wednesday initial quantities of the iPhone 7 Plus have sold out globally. The smaller iPhone 7 has sold out in the jet black color.
Verizon has said its iPhone 7 pre-order volume is within the normal range. However, both Sprint and T-Mobile have said demand is up significantly.
Sprint announced pre-orders of the new iPhones were up more than 375 percent in the first three days compared with last year. T-Mobile said pre-orders are up nearly four times compared with pre-registrations for the iPhone 6S and iPhone 6.
Harrison noted that there are about 700 million iPhone subscribers exiting this year and a lot of them could potentially upgrade their phone.
He said other potential catalysts could be the supply chain raising its production forecast heading into October, ahead of the earnings period. Plus there will be the refresh of other products, like the MacBook, in the fall, he added.
Apple shares have rallied over the past few days, and were up more than 3 percent Thursday in afternoon trading. If the stock closes 2 percent or higher, it would be the fourth day straight of doing so. That hasn't happened since April of 2009.
However, despite the recent rally, shares are still trading at a discount to the S&P 500, Harrison pointed out.
— CNBC's Anita Balakrishnan and Peter Shacknow contributed to this report.