To me, there are two great reasons to invest passively. The first is that it is impossible to time to market. Bargains may come along and you may choose to do some individual stock investment then, but it will be for meaningless amounts of your portfolio (< 5%).
The second is that you are far better off concentrating on your chosen career then trying also to be a stock picker. Doing a better job, at your career, will probably yield much better results then trying to pick stocks. You will likely receive more income that can be funneled into your passive investments, so those extra income dollars compound. This is especially true for those who's active investing result in losses!
What I would do is a little bit at a time, perhaps like 5% of your portfolio per day. You could be very wrong on timing, like perhaps tomorrow is the worst day of the decade to make the trades. Sell your stock, then go with your chosen asset allocation to buy the funds. If it was a horrible time, so what, it was a small part of your portfolio.
On the other hand, doing the above is a form of active investing. You could just "rip the band aide off", sell all stocks and buy the funds. Be done with it.
No one can tell you the best way to do this, again we cannot time the market.
Keep in mind if this is in a taxable account, it could greatly reduce or increase your income due to gains or losses.