These will be available only to those living in New Zealand, and supporters can increase their chances by the above criteria.
The ballot will be drawn in mid-November.
The series starts in Whangarei on June 3, and the first test will be held on June 24.
Test match tickets range in price from $149 to $449. Matches involving the New Zealand Provincial Barbarians, Super Rugby teams and Maori range from $39 to $129. Children's tickets start at $10 for the Barbarians match and $29 for the other non-Test matches. There are no children's prices for the tests.
New Zealand Rugby chief executive Steve Tew said his organisation was committed to making matches as affordable as possible, but acknowledged prices were set higher than for normal Super Rugby matches and domestic tests.
Continued below.
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"We believe we've settled on a fair level of pricing for what is the biggest event New Zealand will host since [the] Rugby World Cup 2011.
"A family of four will be able to see the British and Irish Lions take on their Super Rugby team for under $160, while the tests are priced at about the level of a Rugby World Cup quarter-final or other major international event.
"We believe we've got the balance right - we want to encourage as many New Zealanders as possible to embrace this unique rugby experience as we welcome the legions of Lions fans to our shores once again."
More than 20,000 Lions fans are expected to descend on New Zealand during the series.
"We're aiming at having at least 250,000 tickets across the 10 matches available to buy. The remaining tickets are being sold through official travel and hospitality packages. We're already seeing significant demand for tickets in the UK and Ireland with Lions Rugby Travel likely to sell out their allocation of tickets as part of their Supporter Tours packages."
Ticket facts
350,000 tickets on sale - 250,000 will be available via general public ticket process.
Pre-sales for non-Test matches:
• 3-13 October season ticket holders
• 14-18 October rugby community members
• 21-27 October Team All Blacks members
Public sale for non-Test matches from October 28, 2016.
More than 50 percent of tickets priced under $100.
Test Match Ticket Ballot
Ballots for Test tickets open September 5, close November 1, 2016. Ballot drawn between November 2-16, 2016.
Additional entries in the ballot for:
• Every ticket purchased for the seven non-test matches
• Each purchase of a 2017 Super Rugby team or provincial union season ticket or membership
• Rugby community members
• Team All Blacks members
• Each purchase of a ticket to Wellington Sevens before November 1, 2016