The Geneva-based operations, founded over 200 years ago, have both decided to drop their special statutes and transform themselves into banks almost like any other.
The move is seen as part of a drive to improve transparency and protect the sector from risks associated with scandals such as the Madoff case in the United States, analysts say.
Swiss private banks operate under rules which make the wealthy managing partners personally responsible for the money they manage.
In other words, if the bank gets into trouble, the managing partners can lose all their assets, not just those they have invested in the operation.
Drawn from an elite social circle of Geneva Protestants, the city was the hub of the Reformation five centuries ago, the private bankers have over the centuries refreshed their ranks by tapping wealthy, likeminded members from their own community.
That tradition of unlimited responsibility for those who run private banks has long been seen as a commercial argument for rich customers who want the comfort such a guarantee provides.
Not being listed on the stock exchange, they do not have to publish their results, meaning their business is the preserve of a closed circle of clients.
But from next year, both Pictet and Lombard Odier are to recast themselves as a "corporate partnership", a hybrid status that will make it easier to compare them with fully-listed Swiss players such as Credit Suisse and UBS.
Similar to the "limited company" structure in the British Isles -- with its well-known "Ltd." label -- the structure will enable the banks to tap the investment market while maintaining the managing partners' responsibility.
According to a Pictet spokesman, neither bank will be publicly-listed, and only private investors are to be tapped for capital.
After the reform is in place, the managing partners will only risk the funds they have invested in the bank, rather than having to put all of their personal assets on the line.
"This legal structure allows us to maintain the benefits of a private partnership, such as our independence, strict sense of responsibilities and our long-term management outlook while ensuring that our interests remain aligned with those of our clients," Patrick Odier, senior partner of Lombard Odier,
said in a statement.