Boeing is aiming to begin delivering 787s again in early May.
The 787 has been grounded since mid-January because of smoldering batteries. Federal authorities have approved Boeing's redesigned battery system.
The new battery setup has been installed on 10 787s that belong to airlines, and on nine more that have been built but not delivered, said Boeing Co. Chairman and CEO Jim McNerney on Wednesday.
He said "the bulk" of 787s already in the airlines' possession will get the battery fix by mid-May. Boeing has said each installation will take about five days.
Boeing kept producing the 787 even though it was grounded. But it can only collect the cash from airlines when it delivers the planes - so restarting deliveries is important.
The fix should keep any battery problems "from affecting the airplane or even being noticed by passengers," McNerney said on the company's quarterly earnings conference call.
One 787 experienced a fire after landing, while smoke forced an emergency landing on another. Boeing has gotten clearance from the Federal Aviation Administration for a redesigned battery system that the company says should sharply reduce the risk of a fire. Once the FAA approves the fix on individual planes, airlines can start flying them again.
On Tuesday, United Airlines moved one of its six 787s to a Boeing facility in San Antonio, Texas, so it can get the battery fix.
Despite the 787 troubles, Boeing's net income rose 20 percent in the first quarter.
The big airplane maker earned $1.11 billion, or $1.44 per share. Excluding pension contributions, Boeing would have earned $1.73 per share, well above analyst expectations.
Revenue fell 3 percent to $18.89 billion because Boeing delivered just one 787 before the plane was grounded.
Boeing still expects to meet its financial and delivery targets this year. That includes delivering at least 60 787s. It delivered 137 planes during the quarter, because faster production of 737s and 777s offset the lack of 787 deliveries.
The quarter didn't include any special charges for the 787 or for the automatic government spending cuts that took effect last month.
Profit rose in Boeing's defense and commercial airplane units, even though revenue fell in both.
Boeing shares rose $2.97, or 3.4 percent, to $91.15 in morning trading after rising as high $92.65 earlier. That was the highest level for the shares since December 2007, according to FactSet.