The strike prevented paper manufacturers from exporting their products, and the sector now faces a backlog of orders after mills closed their paper machines.
Stora Enso has now recommenced almost all of its closed production, having shut down six paper machines and two sheeting plants while the strike was on.
A spokeswoman said it would "take weeks to normalise all operations in mills and especially in harbours".
"The stevedores have now stopped their strike, which is great news. We will start closed production when possible. However, while we are currently starting up machines, full production at the mills will only start in a few weeks," she added.
A spokesman for UPM said the company expected to normalise production within the working week.
He added that not all of the company's mills had been shut completely and that the business was discussing product updates with customers on a case-by-case basis.
Martti Savelainen, Sappi mill director in Kirkniemi, Finland, said: "Our employees have reintegrated the mill today (19 March) and in a week's time we will have reached our usual production level."
The strike began on 4 March after talks between union officials and port operators collapsed. At the time, paper manufacturers said the strikes would cost them up to €3m (£2.7m) per day.
The impact of the strike is another blow to the beleaguered Finnish paper industry, which has been hit by overcapacity and raw material price increases over the past few years.