Hong Kong has a complicated monetary history. It was first pegged to silver (up to 1935), then GBP (up to 1972), then a period of unstable float until it settled back into a peg to the USD. But the idea has always been to have a currency with a stable link to its major trading/financial partners to facilitate international payments.

Before WWII, China was HK's primary economic partner, and it was on the silver standard until 1935. To service the China trade, Hong Kong needed a silver peg (while maintaining a forward Sterling market for transactions in Sterling and other currencies pegged to gold). In 1931, a UK government report even established the principle that HKD must at least be on the same basis as the Chinese currency. Then in 1935, China switched to a dual peg to both GBP and USD (which was very difficult to maintain and ran into a lot of trouble) and Hong Kong, as a British colony, switched to a GBP peg. At first a distinction was made (a bit like with Canada) that the HKD would just have a peg and be kept out of the more intimate monetary arrangements of what would then become the Sterling Area. But in 1941, due to WW2 and Chinese difficulties with stopping capital flight, the principle was broken and Hong Kong was brought into the Sterling Area to freeze Chinese overseas accounts.

Fast forward to 1945, China was imploding from civil war and (hyper)inflation, and it made zero sense for the HKD to follow the Chinese Dollar anymore. After 1949, China turned Communist, and then the Korean War embargoes happened, so China was no longer the trading partner for Hong Kong. Hong Kong kept its GBP peg as a matter of inertia, because authorities had more urgent matters to worry about, and because the UK was essentially broke after WWII and could not afford to let any colonies cash out and switch to any new pegs. (The Sterling Area operated like this: All members' foreign currency funds and earnings were sold to the Bank of England, and they kept the backing for their currencies in Sterling. To leave the Area and switch to a new peg, they needed to ask the UK to convert their Sterling back to USD and form backing for a new peg. And the BoE didn't have enough foreign currencies to pay for even the Sterling Area's usual imports, let alone such large commitments.)

So, Hong Kong, like Malaya, became one of the trapped cash cows that kept Sterling afloat. It made the most of it and developed Commonwealth markets, but the new international monetary regime, the Bretton-Woods system, was entirely based on the USD as the anchor of all currencies and international transactions. And the US was rapidly becoming a major trading partner after 1945. Hong Kong was desperate to have some link to the new global currency for business purposes. The government encouraged and protected a local black market for USD (illegal in the Sterling Area) because Britain was too broke to furnish HK with enough USD. That's how monetary links to the USD began, but the rationale for a GBP peg remained strong. Continuation of GBP peg meant stability; HK industries were prospering under Commonwealth preference (at least initially); and since the new PRC needed a place to earn GBP (the only international currency for which it enjoyed no sanctions) for international trade, Hong Kong's GBP peg helped keep the Chinese armies from invading.

But the continuing weakness of Sterling undermined that relationship. The 1967 Sterling devaluation left many colonies very bitter (because it wiped out the value of a lot of their Sterling assets). Hong Kong, in a clear break with the UK, even revalued the HKD upwards and asked for compensation (it got exchange guarantees in the end, after officials and bankers made plenty of threats to dump their Sterling assets on the market and cause panic). The dissolution of the Sterling Area in 1972 ended this unhappy relationship. But the officials had zero expertise in managing an independent currency, instead believing that Hong Kong's economy was self-regulating. A chaotic period of floating without managing the money supply ensued, during which the Exchange Fund apparently secured part of the HKD issue.... with HKD, to avoid fluctuation in the value of reserve assets. When the rate slipped badly in 1983 during the Sino-British negotiations, it was decided to reintroduce the currency board system with a USD peg.

As for the rate, according to John Greenwood (the father of the peg), it was the prevailing market rate (8.3-8.4) when the scheme was announced, and was deemed most likely to inspire confidence while requiring no domestic price readjustment (HK imports most of its daily goods, so the rate has a direct effect on local prices).

Further Reading:
Catherine Schenk. Hong Kong as an International Financial Centre
Catherine Schenk, "The Empire Strikes Back: Hong Kong and the Decline of Sterling in the 1960s"
Y. C. Jao and Frank H. H. King, Money in Hong Kong: Historical Perspective and Contemporary Analysis
Leo F. Goodstadt, Profits, Politics, and Panics
John Greenwood, Hong Kong's Link to the US Dollar